Simplex Method Calculator

Calculator

Examples

Help

Decision Variables

Constraints

Optimization Type

Note: For minimization problems or constraints with ≥ or =, the calculator will automatically convert to standard form. All variables are assumed to be non-negative.

Solution & Steps

No solution yet. Click "Build Input" to set up your problem, then "Solve" to find the solution.

Example Problems

Try these example problems to get started with the simplex method calculator:

Maximization Problem

Maximize Z = 3x₁ + 2x₂ subject to:

x₁ + x₂ ≤ 4

2x₁ + x₂ ≤ 5

x₁, x₂ ≥ 0

Minimization Problem

Minimize Z = 4x₁ + 3x₂ subject to:

2x₁ + x₂ ≥ 10

x₁ + 2x₂ ≥ 8

x₁, x₂ ≥ 0

Mixed Constraints

Maximize Z = 2x₁ + 3x₂ subject to:

x₁ + x₂ ≤ 6

2x₁ + x₂ ≥ 4

x₁ + 2x₂ = 6

x₁, x₂ ≥ 0

How to Use the Calculator

Setting Up the Problem

1. Enter the number of decision variables and constraints

2. Select whether to maximize or minimize the objective function

3. Click "Build Input" to create the input table

Entering Coefficients

1. Fill in the objective function coefficients

2. Enter constraint coefficients and select constraint type (≤, =, ≥)

3. Enter the right-hand side (RHS) values for constraints

Solving and Results

1. Click "Solve" to run the simplex method

2. View the step-by-step solution process

3. Check the optimal solution and objective value

Tips for Better Results

Numerical Stability

• Use reasonable coefficient values (avoid extremely large or small numbers)

• If possible, scale your problem to have coefficients of similar magnitude

Problem Formulation

• Ensure all variables are non-negative

• For minimization problems, the calculator automatically converts to maximization

• All RHS values should be non-negative

Troubleshooting

• If the solution seems incorrect, check your constraint types

• For unbounded problems, review your constraints

• For infeasible problems, check for conflicting constraints