Question

Consider the following linear programming problem: min s.t. x, 2x2 x, 3x, ≥90 8x, 2x, ≥160 3x, 2x, ≥120 x, ≤ 70 2,22≥0 a. write the problem in standard form. identify slack/surplus variables.

Answer 1

To write the linear programming problem in standard form, convert all inequality constraints to equations and add slack or surplus variables as necessary.

Step-by-step explanation:

To write the linear programming problem in standard form, we need to convert all inequality constraints to equations and add slack or surplus variables. The given problem is:

Minimize: s

Subject to:

x + 2x2 + x3 ≥ 90

8x + 2x2 + x3 ≥ 160

3x + 2x2 ≥ 120

x ≤ 70

2,2 ≥ 0

Adding slack variables:

x + 2x2 + x3 + s1 = 90

8x + 2x2 + x3 + s2 = 160

3x + 2x2 + s3 = 120

x + s4 = 70

2,2 + s5 = 0

The problem is now in standard form with slack variables s1, s2, s3, s4, and s5.