Linear Programming Simplex Method Calculator
This calculator helps solve linear programming models with the simplex method. It is useful when a goal must be maximized or minimized. Common goals include profit, cost, output, distance, time, or resource use. The method works with linear objective functions and linear constraints.
What This Tool Does
The tool builds a simplex tableau from your objective function and constraints. It adds slack variables for less than or equal limits. It adds surplus and artificial variables when needed. Then it chooses pivot columns and pivot rows. Each pivot improves the current solution. The process stops when no improving column remains, or when the model cannot be solved.
Why Simplex Is Important
Simplex is a classic optimization method. It checks corner points of a feasible region without drawing every graph. This makes it powerful for larger problems. A business can compare product mixes. A student can verify homework steps. An analyst can test resource allocation plans. The calculator also shows iterations, so the path is easier to audit.
Inputs You Can Enter
You may choose maximization or minimization. You may enter two to four decision variables. You may enter up to six constraints. Each constraint accepts coefficients, a relation symbol, and a right hand side value. The calculator assumes decision variables are non negative. This is the common form for simplex models.
Reading The Results
The answer shows the final objective value and each decision variable. Slack values show unused capacity. Surplus values show excess over a minimum requirement. Artificial values should finish near zero. If an artificial value remains positive, the original model is infeasible.
Best Use Cases
Use this calculator for classroom learning, operations planning, production scheduling, blending problems, diet models, shipping decisions, and resource allocation. It is not meant for nonlinear models. It also does not replace expert review for financial or engineering decisions.
Accuracy Tips
Check every sign before solving. Make sure all coefficients use the same units. Avoid mixing hours, minutes, dollars, and percentages without conversion. If a result seems strange, review the constraints first. Small input mistakes can change the final corner point completely.
They also help compare manual work against answers. Use exported notes for assignments and reports during review.