Simplex Method Calculator

Enter the objective function and constraints in the calculator fields, select Maximize or Minimize, then click Solve. The tool automatically performs all pivot operations and displays the optimal solution.

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.

Choose the number of variables, enter the objective function row, add each constraint row with its RHS value, select your goal (Max/Min), and press Calculate to get the full solution.

Search 'simplex method calculator' online and open any free tool. Enter your linear programming problem, and the calculator applies the simplex algorithm to find the optimal solution automatically.

Set up the initial simplex tableau with decision variables and slack variables. Identify the most negative Cj-Zj value as pivot column, calculate ratios to find pivot row, then perform elementary row operations to iterate.

Open the simplex minimization calculator, select the Minimize option, enter your cost function coefficients and constraint values, then click Solve to get the minimum objective value and optimal variable values.

Zj = sum of (Cbi × aij) for each column j, where Cbi is the objective coefficient of the current basic variable in row i, and aij is the corresponding tableau element in that column.

On a TI-84, store the tableau in a matrix using MATRIX > EDIT, then use row operations via MATRIX > MATH (rowSwap, *row, *row+). Alternatively, use a dedicated simplex app available for TI calculators.

Yes. Online simplex calculators handle the complete algorithm - from initial tableau setup to final optimal solution - including all pivot selections and row operations automatically.

Casio scientific calculators have no built-in simplex function. However, you can manually perform matrix row operations using Casio's Matrix mode to carry out each pivot step.

A full simplex method calculator covers everything: entering the LP problem, setting up the initial tableau, performing all pivot iterations, identifying the optimal basis, and displaying the final solution with all variable values.

The simplex method is an iterative algorithm, developed by George Dantzig in 1947, for solving linear programming problems. It moves from one vertex (corner point) of the feasible region to an adjacent one, improving the objective function at each step until it reaches the optimal solution.

No. Linear programming is the type of problem - optimizing a linear objective subject to linear constraints. The simplex method is one algorithm used to solve linear programming problems; others include the graphical method and interior-point methods.

A slack variable is added to a ≤ constraint to make it an equation, a surplus variable is subtracted from a ≥ constraint, and an artificial variable is added to ≥ and = constraints to provide a starting basic feasible solution. Artificial variables are removed during the Big M or two-phase method.

Both handle artificial variables for ≥ and = constraints. The Big M method uses a single objective with a large penalty constant M, while the two-phase method first minimizes the artificial variables (Phase 1), then optimizes the real objective (Phase 2). They reach the same optimum.

For maximization, the pivot column (entering variable) is the column with the most positive Cj − Zj value. The pivot row (leaving variable) is found by the minimum-ratio test: divide each right-hand-side value by the positive entry in the pivot column and choose the smallest non-negative ratio.

A tableau is optimal when no further improvement is possible. For a maximization problem this happens when every Cj − Zj value is less than or equal to zero; for minimization, when every Cj − Zj is greater than or equal to zero.

Yes. Minimization is solved either by converting it to an equivalent maximization (minimize Z is the same as maximize −Z) or by selecting the most negative Cj − Zj as the entering variable. Constraints of the ≥ type are handled with surplus and artificial variables.

The dual simplex method starts from a tableau that is optimal but infeasible (some right-hand-side values are negative). It selects the leaving variable first (the most negative RHS), then the entering variable by a dual ratio test, restoring feasibility while preserving optimality.

The revised simplex method performs the same iterations as the standard method but stores only the inverse of the basis matrix (B⁻¹) instead of the full tableau. This makes it much more memory-efficient and is the basis of professional linear-programming solvers.

A linear program is unbounded when the objective function can be increased (for maximization) or decreased (for minimization) without limit while still satisfying all constraints. In the simplex method this is detected when the pivot column has no positive entries for the ratio test.

Degeneracy occurs when a basic variable equals zero in a tableau, often because of a tie in the minimum-ratio test. Degeneracy can cause cycling, where the algorithm repeats tableaus without improving the objective; anti-cycling rules such as Bland's rule prevent this.

There is no fixed limit. The graphical method is restricted to two variables, but the simplex method works for any number of decision variables and constraints - from small two-variable textbook problems to industrial models with thousands of variables.

The transportation problem is a special linear program that minimizes the cost of shipping goods from sources to destinations. It can be solved with the general simplex method, but specialized versions (such as the MODI or stepping-stone methods) exploit its structure for efficiency.

The graphical method only works for problems with two variables, because the feasible region must be drawn in two dimensions. The simplex method has no such restriction and can solve problems with any number of variables algebraically, which is why it is the standard approach.