Interactive Simplex LP/MILP Solver

Instructions:
• Set up your linear programming problem using the table below
• Choose constraint types: ≤ (less than or equal), = (equal), ≥ (greater than or equal)
• Select optimization type: Maximize or Minimize
• Select variable type (binary for 0/1 constraints, integer for whole numbers, else continuous)
• Click "Solve" to see step-by-step solution
• Slack/surplus/artificial variables are automatically generated

Ex. (correlates to 'continuous' example below)

    Problem

    Maximize Objective: 
            Z = 3x₁ + 2x₂
    Subject to Constraints: 
            1x₁ + 1x₂ ≤ 4
            2x₁ + 1x₂ ≤ 6
            x₁, x₂ ≥ 0
    

    Becomes

    Maximize Objective: 
            Z = cᵀx
    Where: 
            c = [3]
                [2]
    Subject to Constraints: 
            Ax ≤ b
    Where:      
            A = [1  1]    b = [4]
                [2  1]        [6]
            x ≥ 0
    

    You would implement this problem in the below table as shown
    (slack variables will be handled automatically and shown in the solution):

    Objective
            

        

            

            
Decision Var1
            
Decision Var2
            

            
Right-Hand-Side
        
        

            
Constraint1
            
1
            
1
            
≤
            
4
        
        

            
Constraint2
            
2
            
1
            
≤
            
6
        
        
Objective
            
3
            
2
            

            

        
    

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Ex. (binary, from PMI)

    Problem

    


    Maximize Objective: 
            Z = 17x1 + 22x2 + 12x3 + 8x4 + 10x5 + 15x6
    Subject to Constraints: 
            5x1 + 7x2 + 4x3 + 3x4 + 3x5 + 5x6 ≤ 18
            x1, x2, x3, x4, x5, x6 ∈ { 0,1 }
    

    Becomes

    Maximize NPV Objective: 
            Z = cᵀx (Sum of project NPVs)
    Where: 
            c(Project NPVs) 
            =   [17]
                [22]
                [12]
                [08]
                [10]
                [15]
    Subject to Budget Constraints: 
            Ax ≤ b
    Where:      
            A(project budgets) = [5  7  4  3  3  5]    
            b(portfolio budget) = [18]
            x = 0  OR  x = 1
    

    You would implement this problem in the below table as shown
    (slack variables will be handled automatically and shown in the solution):

    

        

            

            
Project1
            
Project2
            
Project3
            
Project4
            
Project5
            
Project6
            

            
Budget
        
        

            
Budget
            
5
            
7
            
4
            
3
            
3
            
5
            
≤
            
18
        
        

            
NPV
            
17
            
22
            
12
            
8
            
10
            
15
            

            

        
    
    

        Solution