Standard minimization calculator

The calculator may be used to solve the standard minimization problem with two variables and two constraints such as

Minimize P = 3x + 2y subject to the constraints
æ 2 x + 3 y  ³  12 ö
ç 2 x +   y  ³  8  ÷
ç         x  ³  0  ÷
è         y  ³  0  ø
The calculator is intended to teach students the Simplex method and to relieve them from some of the tedious aritmetic. To solve minimization problems with more variables and/or more constraints you should use profesionally written software available for free over the internet and commercially.

Using the calculator

  1. Set up the dual problem.
    Enter the minimization problem and click the "Dual problem" button.
  2. Set up initial Simplex table for the dual problem.
    Click the "Initialize table" button.
  3. To perform pivot operation.
    Click on the "Find pivot" button to locate the pivot element.
    Click on the "Pivot" button to perform the pivot operation.
  4. To see if an optimal solution has been reached.
    If there are negative entries in the last row of the Simplex table then an optimal solution has not been reached and you must repeat step 2.
  5. To obtain the optimal solution.
    If all of the entries in the last row of the Simplex table are nonnegative. Click the "Dual answer" button to read the answer to the dual (maximization) problem. Click the "Primal answer" button to read the answer to the primal (original minimization) problem.
Standard minimization problem

Minimize
C = x + y
subject to the constraints
æ x + y ö
ç x + y ÷
ç x ³ 0                                           ÷
è y ³ 0                                           ø
Dual problem: Standard maximization problem

Maximize
P = u + v
subject to the constraints
æ u + v £ ö
ç u + v £ ÷
ç u ³ 0                                           ÷
è v ³ 0                                           ø
Simplex Table

u v x y P RHS
Simplex Method

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