Simplex Calculator

Enter a linear optimization problem and click solve. The cost function to maximize or minimize must be indicated with "min" or "max". The constraints must be strict inequalities or strict equalities (<=, >=, or =). All variables must be on the left-hand side of all equations. All equations must be on seperate lines. For example:

max 3x1 + x2 + 3x3 2x1 + 3x2 + 5x3 <= 64 x1 - x2 - x3 >= 0 x2 - x3 >= 2

or

min 12x1 + 16x2 x1 + 2x2 >= 40 x1 + x2 = 30 * >= 0

You can also use the * operator to have a constraint be applied to all variables. For example:

min 5x1 - 20x2 -2x1 + 10x2 <= 5 2x1 + 5x2 <= 10 x1 + * >= 0

will become

min 5x1 - 20x2 -2x1 + 10x2 <= 5 2x1 + 5x2 <= 10 x1 + x1 >= 0 x1 + x2 >= 0

Shown below is each tableau used to calculate the result.

Cost function

Pivot elements

Original cost function in phase one