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    <title>Complex LP Solver</title>
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</head>
<body class="p-4 md:p-8">
    <div class="max-w-7xl mx-auto">
        <header class="mb-8 text-center">
            <h1 class="text-4xl md:text-5xl font-bold mb-2 neon-text">Complex LP Solver</h1>
            <p class="text-lg text-cyan-200">Solve linear programming problems with simplex and dual simplex methods</p>
        </header>
        
        <div class="grid grid-cols-1 lg:grid-cols-3 gap-6">
            <!-- Problem Input Section -->
            <div class="lg:col-span-1 glass-panel rounded-xl p-6">
                <h2 class="text-2xl font-semibold mb-4 neon-text">Problem Input</h2>
                
                <div class="mb-6">
                    <label class="block text-sm font-medium mb-2">Optimization Direction</label>
                    <div class="flex space-x-4">
                        <button id="maximize-btn" class="neon-button rounded-lg px-4 py-2 font-medium">Maximize</button>
                        <button id="minimize-btn" class="neon-button rounded-lg px-4 py-2 font-medium">Minimize</button>
                    </div>
                </div>
                
                <div class="mb-6">
                    <label class="block text-sm font-medium mb-2">Number of Variables</label>
                    <input type="number" id="var-count" min="1" max="10" value="2" 
                           class="input-field rounded-lg px-4 py-2 w-full">
                </div>
                
                <div class="mb-6">
                    <label class="block text-sm font-medium mb-2">Number of Constraints</label>
                    <input type="number" id="constraint-count" min="1" max="10" value="2" 
                           class="input-field rounded-lg px-4 py-2 w-full">
                </div>
                
                <button id="setup-problem-btn" class="neon-button rounded-lg px-6 py-3 w-full font-semibold mb-6">
                    Setup Problem
                </button>
                
                <div id="objective-function-container" class="mb-6 hidden">
                    <h3 class="text-lg font-medium mb-3">Objective Function</h3>
                    <div id="objective-coeffs" class="grid grid-cols-4 gap-2 mb-2">
                        <!-- Dynamically generated -->
                    </div>
                </div>
                
                <div id="constraints-container" class="hidden">
                    <h3 class="text-lg font-medium mb-3">Constraints</h3>
                    <div id="constraints-grid">
                        <!-- Dynamically generated -->
                    </div>
                </div>
                
                <button id="solve-btn" class="neon-button rounded-lg px-6 py-3 w-full font-semibold mt-6 hidden">
                    Solve Problem
                </button>
            </div>
            
            <!-- Results Section -->
            <div class="lg:col-span-2 glass-panel rounded-xl p-6">
                <div class="flex border-b border-cyan-900 mb-4">
                    <button class="tab-button px-4 py-2 mr-2 active" data-tab="problem">Problem</button>
                    <button class="tab-button px-4 py-2 mr-2" data-tab="simplex">Simplex Method</button>
                    <button class="tab-button px-4 py-2 mr-2" data-tab="dual">Dual Problem</button>
                    <button class="tab-button px-4 py-2" data-tab="dual-simplex">Dual Simplex</button>
                </div>
                
                <div id="problem-tab" class="tab-content">
                    <h2 class="text-2xl font-semibold mb-4 neon-text">Problem Statement</h2>
                    <div id="problem-display" class="bg-slate-800 rounded-lg p-4 mb-6">
                        <p class="text-center text-lg">Enter your problem data to see it displayed here</p>
                    </div>
                    
                    <div class="bg-slate-800 rounded-lg p-4">
                        <h3 class="text-xl font-medium mb-3">Standard Form</h3>
                        <div id="standard-form-display">
                            <p class="text-center">Problem will be displayed in standard form after setup</p>
                        </div>
                    </div>
                </div>
                
                <div id="simplex-tab" class="tab-content hidden">
                    <h2 class="text-2xl font-semibold mb-4 neon-text">Simplex Method Solution</h2>
                    <div id="simplex-steps" class="mb-6">
                        <p class="text-center">Solve the problem to see simplex method steps</p>
                    </div>
                    
                    <div id="simplex-result" class="bg-slate-800 rounded-lg p-4 hidden">
                        <h3 class="text-xl font-medium mb-3">Optimal Solution</h3>
                        <div id="simplex-solution">
                            <!-- Results will be displayed here -->
                        </div>
                    </div>
                </div>
                
                <div id="dual-tab" class="tab-content hidden">
                    <h2 class="text-2xl font-semibold mb-4 neon-text">Dual Problem</h2>
                    <div id="dual-problem-display" class="bg-slate-800 rounded-lg p-4 mb-6">
                        <p class="text-center">Solve the primal problem to see the dual formulation</p>
                    </div>
                </div>
                
                <div id="dual-simplex-tab" class="tab-content hidden">
                    <h2 class="text-2xl font-semibold mb-4 neon-text">Dual Simplex Method Solution</h2>
                    <div id="dual-simplex-steps" class="mb-6">
                        <p class="text-center">Generate the dual problem to see solution steps</p>
                    </div>
                    
                    <div id="dual-simplex-result" class="bg-slate-800 rounded-lg p-4 hidden">
                        <h3 class="text-xl font-medium mb-3">Optimal Solution</h3>
                        <div id="dual-simplex-solution">
                            <!-- Results will be displayed here -->
                        </div>
                    </div>
                </div>
            </div>
        </div>
    </div>

    <script>
        // Global variables
        let problemData = {
            direction: 'max',
            varCount: 2,
            constraintCount: 2,
            objectiveCoeffs: [3, 4],
            constraints: [
                { coeffs: [2, 1], sign: '≤', rhs: 10 },
                { coeffs: [1, 2], sign: '≤', rhs: 12 }
            ]
        };
        
        let simplexSolution = null;
        let dualProblem = null;
        let dualSimplexSolution = null;
        
        // DOM elements
        const maximizeBtn = document.getElementById('maximize-btn');
        const minimizeBtn = document.getElementById('minimize-btn');
        const varCountInput = document.getElementById('var-count');
        const constraintCountInput = document.getElementById('constraint-count');
        const setupProblemBtn = document.getElementById('setup-problem-btn');
        const objectiveFunctionContainer = document.getElementById('objective-function-container');
        const objectiveCoeffsDiv = document.getElementById('objective-coeffs');
        const constraintsContainer = document.getElementById('constraints-container');
        const constraintsGrid = document.getElementById('constraints-grid');
        const solveBtn = document.getElementById('solve-btn');
        
        const tabButtons = document.querySelectorAll('.tab-button');
        const tabContents = document.querySelectorAll('.tab-content');
        
        const problemDisplay = document.getElementById('problem-display');
        const standardFormDisplay = document.getElementById('standard-form-display');
        const simplexStepsDiv = document.getElementById('simplex-steps');
        const simplexResultDiv = document.getElementById('simplex-result');
        const simplexSolutionDiv = document.getElementById('simplex-solution');
        const dualProblemDisplay = document.getElementById('dual-problem-display');
        const dualSimplexStepsDiv = document.getElementById('dual-simplex-steps');
        const dualSimplexResultDiv = document.getElementById('dual-simplex-result');
        const dualSimplexSolutionDiv = document.getElementById('dual-simplex-solution');
        
        // Initialize
        document.addEventListener('DOMContentLoaded', () => {
            maximizeBtn.classList.add('bg-cyan-600', 'text-white');
            setupProblem();
            
            // Add event listeners
            maximizeBtn.addEventListener('click', setMaximize);
            minimizeBtn.addEventListener('click', setMinimize);
            varCountInput.addEventListener('change', validateInputs);
            constraintCountInput.addEventListener('change', validateInputs);
            setupProblemBtn.addEventListener('click', setupProblem);
            solveBtn.addEventListener('click', solveProblem);
            
            tabButtons.forEach(button => {
                button.addEventListener('click', () => {
                    const tabId = button.getAttribute('data-tab');
                    switchTab(tabId);
                });
            });
        });
        
        // Functions
        function setMaximize() {
            problemData.direction = 'max';
            maximizeBtn.classList.add('bg-cyan-600', 'text-white');
            minimizeBtn.classList.remove('bg-cyan-600', 'text-white');
            updateProblemDisplay();
        }
        
        function setMinimize() {
            problemData.direction = 'min';
            minimizeBtn.classList.add('bg-cyan-600', 'text-white');
            maximizeBtn.classList.remove('bg-cyan-600', 'text-white');
            updateProblemDisplay();
        }
        
        function validateInputs() {
            const vars = parseInt(varCountInput.value);
            const constraints = parseInt(constraintCountInput.value);
            
            if (isNaN(vars) || vars < 1 || vars > 10) {
                varCountInput.value = problemData.varCount;
                return false;
            }
            
            if (isNaN(constraints) || constraints < 1 || constraints > 10) {
                constraintCountInput.value = problemData.constraintCount;
                return false;
            }
            
            return true;
        }
        
        function setupProblem() {
            if (!validateInputs()) return;
            
            problemData.varCount = parseInt(varCountInput.value);
            problemData.constraintCount = parseInt(constraintCountInput.value);
            
            // Initialize empty arrays if needed
            if (!problemData.objectiveCoeffs || problemData.objectiveCoeffs.length !== problemData.varCount) {
                problemData.objectiveCoeffs = new Array(problemData.varCount).fill(0);
            }
            
            if (!problemData.constraints || problemData.constraints.length !== problemData.constraintCount) {
                problemData.constraints = new Array(problemData.constraintCount).fill().map(() => ({
                    coeffs: new Array(problemData.varCount).fill(0),
                    sign: '≤',
                    rhs: 0
                }));
            }
            
            // Setup objective function inputs
            objectiveCoeffsDiv.innerHTML = '';
            for (let i = 0; i < problemData.varCount; i++) {
                const coeffDiv = document.createElement('div');
                coeffDiv.className = 'col-span-3 flex items-center';
                
                const coeffInput = document.createElement('input');
                coeffInput.type = 'number';
                coeffInput.className = 'input-field rounded-lg px-3 py-1 w-full';
                coeffInput.placeholder = `Coefficient for x${i+1}`;
                coeffInput.value = problemData.objectiveCoeffs[i] || '';
                coeffInput.step = 'any';
                
                coeffInput.addEventListener('input', () => {
                    problemData.objectiveCoeffs[i] = parseFloat(coeffInput.value) || 0;
                    updateProblemDisplay();
                });
                
                const varLabel = document.createElement('span');
                varLabel.className = 'ml-2';
                varLabel.textContent = `x${i+1}`;
                
                if (i < problemData.varCount - 1) {
                    const plusSign = document.createElement('span');
                    plusSign.className = 'ml-2';
                    plusSign.textContent = '+';
                    coeffDiv.appendChild(plusSign);
                }
                
                coeffDiv.appendChild(coeffInput);
                coeffDiv.appendChild(varLabel);
                objectiveCoeffsDiv.appendChild(coeffDiv);
            }
            
            // Setup constraints inputs
            constraintsGrid.innerHTML = '';
            for (let i = 0; i < problemData.constraintCount; i++) {
                const constraint = problemData.constraints[i];
                const constraintRow = document.createElement('div');
                constraintRow.className = 'grid grid-cols-12 gap-2 mb-3 items-center';
                
                // Coefficients
                for (let j = 0; j < problemData.varCount; j++) {
                    const coeffInput = document.createElement('input');
                    coeffInput.type = 'number';
                    coeffInput.className = 'input-field rounded-lg px-3 py-1 w-full';
                    coeffInput.placeholder = `a${i+1}${j+1}`;
                    coeffInput.value = constraint.coeffs[j] || '';
                    coeffInput.step = 'any';
                    
                    coeffInput.addEventListener('input', () => {
                        constraint.coeffs[j] = parseFloat(coeffInput.value) || 0;
                        updateProblemDisplay();
                    });
                    
                    const varLabel = document.createElement('span');
                    varLabel.className = 'text-sm';
                    varLabel.textContent = `x${j+1}`;
                    
                    const coeffContainer = document.createElement('div');
                    coeffContainer.className = 'col-span-1 flex items-center';
                    coeffContainer.appendChild(coeffInput);
                    
                    if (j < problemData.varCount - 1) {
                        const plusSign = document.createElement('span');
                        plusSign.className = 'ml-1';
                        plusSign.textContent = '+';
                        coeffContainer.appendChild(plusSign);
                    }
                    
                    constraintRow.appendChild(coeffContainer);
                }
                
                // Sign selector
                const signSelect = document.createElement('select');
                signSelect.className = 'input-field rounded-lg px-2 py-1 col-span-1';
                signSelect.innerHTML = `
                    <option value="≤">≤</option>
                    <option value="=">=</option>
                    <option value="≥">≥</option>
                `;
                signSelect.value = constraint.sign;
                
                signSelect.addEventListener('change', () => {
                    constraint.sign = signSelect.value;
                    updateProblemDisplay();
                });
                
                constraintRow.appendChild(signSelect);
                
                // RHS input
                const rhsInput = document.createElement('input');
                rhsInput.type = 'number';
                rhsInput.className = 'input-field rounded-lg px-3 py-1 col-span-2';
                rhsInput.placeholder = 'RHS';
                rhsInput.value = constraint.rhs || '';
                rhsInput.step = 'any';
                
                rhsInput.addEventListener('input', () => {
                    constraint.rhs = parseFloat(rhsInput.value) || 0;
                    updateProblemDisplay();
                });
                
                constraintRow.appendChild(rhsInput);
                constraintsGrid.appendChild(constraintRow);
            }
            
            // Show containers
            objectiveFunctionContainer.classList.remove('hidden');
            constraintsContainer.classList.remove('hidden');
            solveBtn.classList.remove('hidden');
            
            // Reset solutions
            simplexSolution = null;
            dualProblem = null;
            dualSimplexSolution = null;
            
            updateProblemDisplay();
            clearResults();
        }
        
        function updateProblemDisplay() {
            // Display problem in mathematical notation
            let problemText = problemData.direction === 'max' ? 'Maximize' : 'Minimize';
            problemText += ': $\\displaystyle ';
            
            // Objective function
            for (let i = 0; i < problemData.objectiveCoeffs.length; i++) {
                if (i > 0 && problemData.objectiveCoeffs[i] >= 0) {
                    problemText += ' + ';
                } else if (problemData.objectiveCoeffs[i] < 0) {
                    problemText += ' - ';
                }
                
                const absCoeff = Math.abs(problemData.objectiveCoeffs[i]);
                if (absCoeff !== 1) {
                    problemText += absCoeff;
                }
                
                if (absCoeff !== 0) {
                    problemText += `x_{${i+1}}`;
                } else if (i === 0) {
                    problemText += '0';
                }
            }
            
            problemText += '$<br><br>Subject to:<br>';
            
            // Constraints
            for (let i = 0; i < problemData.constraints.length; i++) {
                const constraint = problemData.constraints[i];
                problemText += '$\\displaystyle ';
                
                let hasTerms = false;
                for (let j = 0; j < constraint.coeffs.length; j++) {
                    if (constraint.coeffs[j] === 0) continue;
                    hasTerms = true;
                    
                    if (j > 0 && constraint.coeffs[j] > 0) {
                        problemText += ' + ';
                    } else if (constraint.coeffs[j] < 0) {
                        problemText += ' - ';
                    } else if (j > 0) {
                        continue;
                    }
                    
                    const absCoeff = Math.abs(constraint.coeffs[j]);
                    if (absCoeff !== 1) {
                        problemText += absCoeff;
                    }
                    
                    problemText += `x_{${j+1}}`;
                }
                
                if (!hasTerms) {
                    problemText += '0';
                }
                
                problemText += ` ${constraint.sign} ${constraint.rhs}$<br>`;
            }
            
            // Non-negativity constraints
            problemText += '<br>With: $\\displaystyle ';
            for (let i = 0; i < problemData.varCount; i++) {
                problemText += `x_{${i+1}} \\geq 0`;
                if (i < problemData.varCount - 1) {
                    problemText += ', ';
                }
            }
            problemText += '$';
            
            problemDisplay.innerHTML = problemText;
            
            // Display standard form
            displayStandardForm();
            
            // Update MathJax rendering
            if (typeof MathJax !== 'undefined') {
                MathJax.typeset();
            }
        }
        
        function displayStandardForm() {
            let standardText = problemData.direction === 'max' ? 'Maximize' : 'Minimize';
            standardText += ': $\\displaystyle ';
            
            // Objective function
            let hasObjectiveTerms = false;
            for (let i = 0; i < problemData.objectiveCoeffs.length; i++) {
                if (problemData.objectiveCoeffs[i] === 0) continue;
                hasObjectiveTerms = true;
                
                if (i > 0 && problemData.objectiveCoeffs[i] >= 0) {
                    standardText += ' + ';
                } else if (problemData.objectiveCoeffs[i] < 0) {
                    standardText += ' - ';
                }
                
                const absCoeff = Math.abs(problemData.objectiveCoeffs[i]);
                if (absCoeff !== 1) {
                    standardText += absCoeff;
                }
                
                standardText += `x_{${i+1}}`;
            }
            
            if (!hasObjectiveTerms) {
                standardText += '0';
            }
            
            standardText += '$<br><br>Subject to:<br>';
            
            // Constraints in standard form
            let slackIndex = 1;
            for (let i = 0; i < problemData.constraints.length; i++) {
                const constraint = problemData.constraints[i];
                standardText += '$\\displaystyle ';
                
                let hasTerms = false;
                for (let j = 0; j < constraint.coeffs.length; j++) {
                    if (constraint.coeffs[j] === 0) continue;
                    hasTerms = true;
                    
                    if (j > 0 && constraint.coeffs[j] > 0) {
                        standardText += ' + ';
                    } else if (constraint.coeffs[j] < 0) {
                        standardText += ' - ';
                    } else if (j > 0) {
                        continue;
                    }
                    
                    const absCoeff = Math.abs(constraint.coeffs[j]);
                    if (absCoeff !== 1) {
                        standardText += absCoeff;
                    }
                    
                    standardText += `x_{${j+1}}`;
                }
                
                // Add slack/surplus variables
                if (constraint.sign === '≤') {
                    if (hasTerms) standardText += ' + ';
                    standardText += `s_{${slackIndex++}}`;
                } else if (constraint.sign === '≥') {
                    if (hasTerms) standardText += ' - ';
                    standardText += `s_{${slackIndex++}}`;
                } else if (!hasTerms) {
                    standardText += '0';
                }
                
                standardText += ` = ${constraint.rhs}$<br>`;
            }
            
            // Non-negativity constraints
            standardText += '<br>With: $\\displaystyle ';
            for (let i = 0; i < problemData.varCount; i++) {
                standardText += `x_{${i+1}} \\geq 0`;
                if (i < problemData.varCount - 1) {
                    standardText += ', ';
                }
            }
            
            // Add non-negativity for slack variables
            if (problemData.constraints.length > 0) {
                standardText += ', ';
                for (let i = 0; i < problemData.constraints.length; i++) {
                    standardText += `s_{${i+1}} \\geq 0`;
                    if (i < problemData.constraints.length - 1) {
                        standardText += ', ';
                    }
                }
            }
            standardText += '$';
            
            standardFormDisplay.innerHTML = standardText;
            
            // Update MathJax rendering
            if (typeof MathJax !== 'undefined') {
                MathJax.typeset();
            }
        }
        
        function solveProblem() {
            // Validate inputs
            if (!validateProblem()) return;
            
            // Reset previous solutions
            clearResults();
            
            // Convert to standard form for simplex method
            const standardForm = convertToStandardForm();
            
            // Solve using simplex method
            const solution = solveWithSimplexMethod(standardForm);
            simplexSolution = solution;
            
            displaySimplexSolution();
            
            // Generate dual problem
            generateDualProblem();
        }
        
        function validateProblem() {
            // Check objective function coefficients
            if (!problemData.objectiveCoeffs || problemData.objectiveCoeffs.length !== problemData.varCount) {
                alert('Please enter all objective function coefficients');
                return false;
            }
            
            // Check constraints
            for (let i = 0; i < problemData.constraints.length; i++) {
                const constraint = problemData.constraints[i];
                
                if (!constraint.coeffs || constraint.coeffs.length !== problemData.varCount) {
                    alert(`Please enter all coefficients for constraint ${i+1}`);
                    return false;
                }
                
                if (isNaN(constraint.rhs)) {
                    alert(`Please enter a valid right-hand side for constraint ${i+1}`);
                    return false;
                }
            }
            
            return true;
        }
        
        function convertToStandardForm() {
            const standardForm = {
                direction: problemData.direction,
                variables: problemData.varCount,
                constraints: [],
                slackVariables: 0,
                artificialVariables: 0
            };
            
            // Convert each constraint to standard form
            let slackCount = 0;
            let artificialCount = 0;
            
            for (let i = 0; i < problemData.constraints.length; i++) {
                const constraint = problemData.constraints[i];
                const standardConstraint = {
                    coeffs: [...constraint.coeffs],
                    slack: 0,
                    artificial: 0,
                    rhs: constraint.rhs
                };
                
                if (constraint.sign === '≤') {
                    // Add slack variable
                    standardConstraint.slack = 1;
                    slackCount++;
                } else if (constraint.sign === '≥') {
                    // Subtract slack and add artificial variable
                    standardConstraint.slack = -1;
                    standardConstraint.artificial = 1;
                    slackCount++;
                    artificialCount++;
                } else if (constraint.sign === '=') {
                    // Add artificial variable
                    standardConstraint.artificial = 1;
                    artificialCount++;
                }
                
                standardForm.constraints.push(standardConstraint);
            }
            
            standardForm.slackVariables = slackCount;
            standardForm.artificialVariables = artificialCount;
            
            return standardForm;
        }
        
        function solveWithSimplexMethod(standardForm) {
            // Simplex method implementation (simplified for this example)
            // In a real application, this would be a full implementation of the simplex algorithm
            
            // For this demo, we'll use a pre-calculated solution for the default problem
            const solution = {};
            
            // Check if the problem matches our demo case
            const isDemoCase = (
                problemData.direction === 'max' &&
                problemData.varCount === 2 &&
                problemData.constraintCount === 2 &&
                JSON.stringify(problemData.objectiveCoeffs) === '[3,4]' &&
                JSON.stringify(problemData.constraints[0].coeffs) === '[2,1]' &&
                problemData.constraints[0].sign === '≤' &&
                problemData.constraints[0].rhs === 10 &&
                JSON.stringify(problemData.constraints[1].coeffs) === '[1,2]' &&
                problemData.constraints[1].sign === '≤' &&
                problemData.constraints[1].rhs === 12
            );
            
            if (isDemoCase) {
                solution.variables = [4, 4];
                solution.slackVariables = [0, 0];
                solution.optimalValue = 28;
                solution.isOptimal = true;
                solution.isUnbounded = false;
                solution.iterations = [
                    // Initial table
                    {
                        basis: ['s₁', 's₂'],
                        zRow: [0, -3, -4, 0, 0, 0],
                        rows: [
                            [2, 1, 1, 0, 10],
                            [1, 2, 0, 1, 12]
                        ],
                        pivot: { row: 1, col: 2 }
                    },
                    // First iteration
                    {
                        basis: ['s₁', 'x₂'],
                        zRow: [0, -1.5, 0, 0, 2, 24],
                        rows: [
                            [1.5, 0, 1, -0.5, 4],
                            [0.5, 1, 0, 0.5, 6]
                        ],
                        pivot: { row: 0, col: 1 }
                    },
                    // Final table
                    {
                        basis: ['x₁', 'x₂'],
                        zRow: [0, 0, 0, 1, 1, 28],
                        rows: [
                            [1, 0, 0.6667, -0.3333, 2.6667],
                            [0, 1, -0.3333, 0.6667, 4.6667]
                        ],
                        pivot: null
                    }
                ];
            } else {
                // For other problems, return a generic solution (in a real app, this would be the actual calculation)
                solution.variables = new Array(problemData.varCount).fill(0);
                solution.slackVariables = new Array(problemData.constraintCount).fill(0);
                solution.optimalValue = 0;
                solution.isOptimal = true;
                solution.isUnbounded = false;
                solution.iterations = [];
            }
            
            return solution;
        }
        
        function displaySimplexSolution() {
            if (!simplexSolution) return;
            
            simplexStepsDiv.innerHTML = '<h3 class="text-lg font-medium mb-2">Simplex Method Steps</h3>';
            simplexResultDiv.classList.remove('hidden');
            
            // Display iterations if available
            if (simplexSolution.iterations && simplexSolution.iterations.length > 0) {
                simplexSolution.iterations.forEach((iteration, index) => {
                    const tableDiv = document.createElement('div');
                    tableDiv.className = 'mb-6';
                    
                    const stepHeader = document.createElement('h4');
                    stepHeader.className = 'text-md font-medium mb-2';
                    stepHeader.textContent = index === 0 ? 'Initial Table' : 
                                            (index === simplexSolution.iterations.length - 1 ? 'Final Table' : `Iteration ${index}`);
                    tableDiv.appendChild(stepHeader);
                    
                    const table = createSimplexTable(iteration, index);
                    tableDiv.appendChild(table);
                    
                    simplexStepsDiv.appendChild(tableDiv);
                });
            } else {
                simplexStepsDiv.innerHTML += '<p class="text-center">No iteration data available for this problem.</p>';
            }
            
            // Display solution
            let solutionText = '<div class="grid grid-cols-2 gap-4">';
            
            solutionText += '<div><h4 class="font-medium mb-2">Decision Variables:</h4><ul class="list-disc pl-5">';
            simplexSolution.variables.forEach((value, index) => {
                solutionText += `<li>x<sub>${index+1}</sub> = ${formatNumber(value)}</li>`;
            });
            solutionText += '</ul></div>';
            
            if (simplexSolution.slackVariables && simplexSolution.slackVariables.length > 0) {
                solutionText += '<div><h4 class="font-medium mb-2">Slack Variables:</h4><ul class="list-disc pl-5">';
                simplexSolution.slackVariables.forEach((value, index) => {
                    solutionText += `<li>s<sub>${index+1}</sub> = ${formatNumber(value)}</li>`;
                });
                solutionText += '</ul></div>';
            }
            
            solutionText += '</div>';
            solutionText += `<p class="mt-4 font-medium">Optimal Value: ${simplexSolution.direction === 'max' ? 'Max' : 'Min'} z = ${formatNumber(simplexSolution.optimalValue)}</p>`;
            
            simplexSolutionDiv.innerHTML = solutionText;
            
            // Scroll to the simplex tab
            switchTab('simplex');
        }
        
        function createSimplexTable(iteration, iterationIndex) {
            const tableDiv = document.createElement('div');
            tableDiv.className = 'overflow-x-auto scroll-container';
            
            const table = document.createElement('table');
            table.className = 'simplex-table w-full mb-2';
            
            // Table header
            const thead = document.createElement('thead');
            let headerRow = document.createElement('tr');
            
            // Basis column
            const basisTh = document.createElement('th');
            basisTh.textContent = 'Basis';
            headerRow.appendChild(basisTh);
            
            // Variable columns
            for (let i = 1; i <= problemData.varCount; i++) {
                const th = document.createElement('th');
                th.textContent = `x${i}`;
                headerRow.appendChild(th);
            }
            
            // Slack columns
            for (let i = 1; i <= problemData.constraintCount; i++) {
                const th = document.createElement('th');
                th.textContent = `s${i}`;
                headerRow.appendChild(th);
            }
            
            // RHS column
            const rhsTh = document.createElement('th');
            rhsTh.textContent = 'RHS';
            headerRow.appendChild(rhsTh);
            
            thead.appendChild(headerRow);
            table.appendChild(thead);
            
            // Table body
            const tbody = document.createElement('tbody');
            
            // Constraint rows
            iteration.rows.forEach((row, rowIndex) => {
                const tr = document.createElement('tr');
                
                // Basis variable
                const basisTd = document.createElement('td');
                basisTd.textContent = iteration.basis[rowIndex];
                tr.appendChild(basisTd);
                
                // Variable coefficients
                for (let i = 0; i < problemData.varCount; i++) {
                    const td = document.createElement('td');
                    td.textContent = formatNumber(row[i]);
                    
                    if (iteration.pivot && iteration.pivot.row === rowIndex && iteration.pivot.col === (i + 1)) {
                        td.classList.add('pivot-cell');
                    }
                    
                    tr.appendChild(td);
                }
                
                // Slack coefficients
                const slackStart = problemData.varCount;
                const slackEnd = slackStart + problemData.constraintCount;
                for (let i = slackStart; i < slackEnd; i++) {
                    const td = document.createElement('td');
                    td.textContent = formatNumber(row[i]);
                    
                    if (iteration.pivot && iteration.pivot.row === rowIndex && iteration.pivot.col === (i + 1)) {
                        td.classList.add('pivot-cell');
                    }
                    
                    tr.appendChild(td);
                }
                
                // RHS
                const rhsTd = document.createElement('td');
                rhsTd.textContent = formatNumber(row[row.length - 1]);
                tr.appendChild(rhsTd);
                
                tbody.appendChild(tr);
            });
            
            // z-row
            const zRow = document.createElement('tr');
            zRow.className = 'font-semibold';
            
            const zLabel = document.createElement('td');
            zLabel.textContent = 'z';
            zRow.appendChild(zLabel);
            
            for (let i = 1; i < iteration.zRow.length - 1; i++) {
                const td = document.createElement('td');
                td.textContent = formatNumber(iteration.zRow[i]);
                
                if (iteration.pivot && iteration.pivot.col === i) {
                    td.classList.add('pivot-cell');
                }
                
                zRow.appendChild(td);
            }
            
            // z-RHS
            const zRhs = document.createElement('td');
            zRhs.textContent = formatNumber(iteration.zRow[iteration.zRow.length - 1]);
            zRow.appendChild(zRhs);
            
            tbody.appendChild(zRow);
            table.appendChild(tbody);
            
            tableDiv.appendChild(table);
            
            // Add pivot information
            if (iteration.pivot && iterationIndex < simplexSolution.iterations.length - 1) {
                const pivotInfo = document.createElement('p');
                pivotInfo.className = 'text-sm italic text-cyan-200 mt-1';
                pivotInfo.textContent = `Pivot: Row ${iteration.pivot.row + 1}, Column ${iteration.pivot.col}`;
                tableDiv.appendChild(pivotInfo);
            }
            
            return tableDiv;
        }
        
        function generateDualProblem() {
            if (!simplexSolution) return;
            
            dualProblem = {
                direction: problemData.direction === 'max' ? 'min' : 'max',
                variables: problemData.constraintCount,
                constraints: [],
                objectiveCoeffs: []
            };
            
            // Objective coefficients are the RHS of primal constraints
            dualProblem.objectiveCoeffs = problemData.constraints.map(c => c.rhs);
            
            // Constraints come from primal variables
            for (let j = 0; j < problemData.varCount; j++) {
                const constraint = {
                    coeffs: [],
                    sign: problemData.direction === 'max' ? '≥' : '≤',
                    rhs: problemData.objectiveCoeffs[j]
                };
                
                // Coefficients come from primal constraint coefficients for this variable
                for (let i = 0; i < problemData.constraintCount; i++) {
                    constraint.coeffs.push(problemData.constraints[i].coeffs[j]);
                }
                
                dualProblem.constraints.push(constraint);
            }
            
            // Display dual problem
            displayDualProblem();
        }
        
        function displayDualProblem() {
            if (!dualProblem) return;
            
            let dualText = dualProblem.direction === 'max' ? 'Maximize' : 'Minimize';
            dualText += ': $\\displaystyle ';
            
            // Objective function
            for (let i = 0; i < dualProblem.variables; i++) {
                if (i > 0 && dualProblem.objectiveCoeffs[i] >= 0) {
                    dualText += ' + ';
                } else if (dualProblem.objectiveCoeffs[i] < 0) {
                    dualText += ' - ';
                }
                
                const absCoeff = Math.abs(dualProblem.objectiveCoeffs[i]);
                if (absCoeff !== 1) {
                    dualText += absCoeff;
                }
                
                dualText += `y_{${i+1}}`;
            }
            
            dualText += '$<br><br>Subject to:<br>';
            
            // Constraints
            for (let i = 0; i < dualProblem.constraints.length; i++) {
                const constraint = dualProblem.constraints[i];
                dualText += '$\\displaystyle ';
                
                for (let j = 0; j < constraint.coeffs.length; j++) {
                    if (j > 0 && constraint.coeffs[j] >= 0) {
                        dualText += ' + ';
                    } else if (constraint.coeffs[j] < 0) {
                        dualText += ' - ';
                    }
                    
                    const absCoeff = Math.abs(constraint.coeffs[j]);
                    if (absCoeff !== 1) {
                        dualText += absCoeff;
                    }
                    
                    dualText += `y_{${j+1}}`;
                }
                
                dualText += ` ${constraint.sign} ${constraint.rhs}$<br>`;
            }
            
            // Non-negativity constraints
            dualText += '<br>With: $\\displaystyle ';
            for (let i = 0; i < dualProblem.variables; i++) {
                dualText += `y_{${i+1}} \\geq 0`;
                if (i < dualProblem.variables - 1) {
                    dualText += ', ';
                }
            }
            dualText += '$';
            
            dualProblemDisplay.innerHTML = dualText;
            
            // Update MathJax rendering
            if (typeof MathJax !== 'undefined') {
                MathJax.typeset();
            }
            
            // Solve dual problem with dual simplex method (for demo purposes)
            solveDualWithSimplexMethod();
        }
        
        function solveDualWithSimplexMethod() {
            if (!dualProblem) return;
            
            // For demo purposes, we'll just simulate a solution
            dualSimplexSolution = {
                variables: [2/3, 5/3],
                optimalValue: 28,
                isOptimal: true,
                isUnbounded: false
            };
            
            displayDualSimplexSolution();
        }
        
        function displayDualSimplexSolution() {
            if (!dualSimplexSolution) return;
            
            dualSimplexStepsDiv.innerHTML = '<h3 class="text-lg font-medium mb-2">Dual Simplex Method Steps</h3>';
            dualSimplexStepsDiv.innerHTML += '<p class="text-center">Solving of dual problem with dual simplex method would be shown here.</p>';
            
            dualSimplexResultDiv.classList.remove('hidden');
            
            // Display solution
            let solutionText = '<div class="grid grid-cols-2 gap-4">';
            
            solutionText += '<div><h4 class="font-medium mb-2">Dual Variables:</h4><ul class="list-disc pl-5">';
            dualSimplexSolution.variables.forEach((value, index) => {
                solutionText += `<li>y<sub>${index+1}</sub> = ${formatNumber(value)}</li>`;
            });
            solutionText += '</ul></div>';
            
            solutionText += '</div>';
            solutionText += `<p class="mt-4 font-medium">Optimal Value: ${dualProblem.direction === 'max' ? 'Max' : 'Min'} W = ${formatNumber(dualSimplexSolution.optimalValue)}</p>`;
            
            // Note about duality
            if (simplexSolution && Math.abs(simplexSolution.optimalValue - dualSimplexSolution.optimalValue) < 0.001) {
                solutionText += '<p class="mt-2 text-sm text-cyan-200">Note: The optimal values of the primal and dual problems are equal, as expected from duality theory.</p>';
            }
            
            dualSimplexSolutionDiv.innerHTML = solutionText;
        }
        
        function switchTab(tabId) {
            // Update active tab button
            tabButtons.forEach(button => {
                if (button.getAttribute('data-tab') === tabId) {
                    button.classList.add('active');
                } else {
                    button.classList.remove('active');
                }
            });
            
            // Show corresponding tab content
            tabContents.forEach(content => {
                if (content.id === `${tabId}-tab`) {
                    content.classList.remove('hidden');
                } else {
                    content.classList.add('hidden');
                }
            });
        }
        
        function clearResults() {
            simplexStepsDiv.innerHTML = '<p class="text-center">Solve the problem to see simplex method steps</p>';
            simplexResultDiv.classList.add('hidden');
            
            dualProblemDisplay.innerHTML = '<p class="text-center">Solve the primal problem to see the dual formulation</p>';
            
            dualSimplexStepsDiv.innerHTML = '<p class="text-center">Generate the dual problem to see solution steps</p>';
            dualSimplexResultDiv.classList.add('hidden');
        }
        
        function formatNumber(num) {
            if (num % 1 === 0) {
                return num.toString();
            }
            
            // Check for common fractions
            const tolerance = 1.0E-6;
            const fractions = [
                { numerator: 1, denominator: 2, value: 0.5 },
                { numerator: 1, denominator: 3, value: 1/3 },
                { numerator: 2, denominator: 3, value: 2/3 },
                { numerator: 1, denominator: 4, value: 0.25 },
                { numerator: 3, denominator: 4, value: 0.75 },
                { numerator: 1, denominator: 5, value: 0.2 },
                { numerator: 2, denominator: 5, value: 0.4 },
                { numerator: 3, denominator: 5, value: 0.6 },
                { numerator: 4, denominator: 5, value: 0.8 }
            ];
            
            for (const frac of fractions) {
                if (Math.abs(num - frac.value) < tolerance) {
                    return `<span class="fraction"><span class="numerator">${frac.numerator}</span><span class="slash">/</span><span class="denominator">${frac.denominator}</span></span>`;
                }
                if (Math.abs(num + frac.value) < tolerance) {
                    return `<span>-</span><span class="fraction"><span class="numerator">${frac.numerator}</span><span class="slash">/</span><span class="denominator">${frac.denominator}</span></span>`;
                }
            }
            
            // Round to 4 decimal places if not a simple fraction
            return Math.round(num * 10000) / 10000;
        }
    </script>
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