linear programming simplex method example

Given a system of m linear equations with n variables (m < n). Standard form is the baseline format for all linear programs before solving for the optimal solution and has three requirements: (1) must be a maximization problem, (2) all linear constraints must be in a less-than-or-equal-to inequality, (3) all variables are non-negative. Standard Form of a maximization problem in two variables

Then, 2x 1 + 3x 2 - s = 5 s is the surplus variable If the inequality is ≥(greater than or equal), then we subtract a surplus variable - S to change ≥ to =.įor example: 2x 1 + 3x 2 ≥ 5 is an inequality.

Then, 2x 1 + x 2 + s = 3 s is the slack variable If the inequality is ≤ (less than or equal), then we add a slack variable + S to change ≤ to =.įor example: 2x 1 + x 2 ≤ 3 is an inequality. Surplus variables are variables subtracted into the linear constraints of a linear program to transform them from inequality constraints to equality constraints. Slack variables are additional variables that are introduced into the linear constraints of a linear program to transform them from inequality constraints to equality constraints. Using the tableau and pivot variables, an optimal solution can be reached. To use the Simplex method, a given linear programming model needs to be in standard form, where slack variables can then be introduced. The method produces an optimal solution to satisfy the given constraints and produce a maximum zeta value. The Simplex method is an approach for determining the optimal value of a linear program by hand.

Linear programming simplex method example