Simplex Method Calculator with Steps
Free simplex method calculator with steps: enter your objective and constraints and see every tableau, Cj-Zj row, ratio test and pivot until the optimal solution.
Simplex Calculator
How Simplex Method Calculator Works
Enter the LP Problem
Type the objective function coefficients and every constraint row with its right-hand-side value.
Choose Maximize or Minimize
Pick your optimization goal. The tool builds the initial tableau with slack variables automatically.
Run the Pivot Iterations
The calculator identifies pivot column by Cj-Zj, computes ratios, performs elementary row operations until optimal.
Read the Optimal Solution
Final tableau displays optimal variable values, Zj row, and the maximum/minimum objective value.
Sample Simplex Tableau Output
Example tableau iteration for a 2-variable maximization problem
| Basis | x1 | x2 | s1 | s2 | RHS | Cj-Zj |
|---|---|---|---|---|---|---|
| x1 | 14 | 0 | 0 | 1 | 14 | 0 |
| x2 | 7 | 1 | 0 | 0 | 7 | 5 |
| Zj | 35 | 5 | 0 | 0 | 35 |
See Every Simplex Step
This simplex method calculator with steps shows the full working - not just the final answer. It builds the initial tableau, marks the pivot column (most positive Cj − Zj) and pivot row (minimum ratio), and performs the elementary row operations for each iteration until the tableau is optimal. Watching each pivot makes the algorithm easy to learn for exams and homework.
When to Use It
Use the step-by-step calculator whenever you need to understand or verify the simplex process by hand. Every tableau is displayed with the Zj and Cj − Zj rows and the ratio test, so you can reproduce the same steps on paper or check a TI-84 calculation.
Worked Example: Simplex Method Step by Step
Maximize Z = 5x1 + 4x2 subject to 6x1 + 4x2 <= 24, x1 + 2x2 <= 6, and x1, x2 >= 0. Add slack variables s1 and s2 to turn each inequality into an equation: 6x1 + 4x2 + s1 = 24 and x1 + 2x2 + s2 = 6. The initial basic feasible solution is x1 = 0, x2 = 0, s1 = 24, s2 = 6 with Z = 0.
Iteration 1: Choose the Pivot
In the first tableau the Cj - Zj row is 5 for x1 and 4 for x2, so x1 (the largest positive value) enters the basis. The minimum ratio test gives 24 / 6 = 4 for row 1 and 6 / 1 = 6 for row 2, so s1 leaves and the pivot element is 6. After dividing row 1 by 6 and clearing the x1 column, the new solution is x1 = 4, Z = 20.
Iteration 2: Reaching the Optimal Solution
Now Cj - Zj for x2 is 4 - 5 x (2/3) = 2/3, which is still positive, so x2 enters. The ratios are 4 / (2/3) = 6 and 2 / (4/3) = 1.5, so s2 leaves. After this pivot every Cj - Zj value is zero or negative, which means the tableau is optimal: x1 = 3, x2 = 1.5 and the maximum Z = 21. The calculator above shows each of these tableaus automatically.
Why Seeing Every Step Matters
Most homework and exam questions are graded on the working, not only the final answer. A simplex method calculator with steps lets you compare your own tableau line by line, find exactly where an arithmetic slip happened, and understand why a variable enters or leaves the basis. Use it to check assignments, prepare for operations research exams, or verify results from Excel Solver.
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Frequently Asked Questions
How to solve simplex method on calculator?
Input your LP variables, coefficients, and constraints. The simplex calculator runs through each tableau iteration and shows you the step-by-step pivot process until reaching the optimal solution.
What does a step-by-step simplex calculator show?
It displays the initial tableau with slack variables, identifies the pivot column and row, performs elementary row operations, and shows the updated tableau for every iteration until the optimal solution is found.
Does this calculator show every iteration?
Yes. It displays the initial tableau and each subsequent tableau, highlighting the pivot column and pivot row, plus the Zj and Cj-Zj rows, until the optimal tableau is reached.
Can I use it to check my homework?
Absolutely. Enter the same problem you solved by hand and compare each tableau and the final optimal values to find any arithmetic mistakes.
What format should I enter the objective in?
Use the form like 3x1 + 5x2, with one constraint per line such as x1 + 2x2 <= 14. The calculator parses the coefficients automatically.