Chapter 4, Problem 4RP

Explanation of Solution

Optimal solution:

• Consider the following linear programing problem:
  • min z= 5x₁-x₂
• Subject to the constraints:
  • x₁-3x₂ ≤ 1
  • x₁-4x₂ ≤ 3
  • x₁, x₂  ≥ 0
• Consider s₁ and s₂ are the two slack variables.
• Add each of the slack variable to each constraint when it is less than or equal to type.
• Here, the given two constraints are less than or equal to type, then we add these two slack variables to make it as standard form and at the same time add these variables to the objective function with 0 quantity weight.
• Therefore, the standard form of the LP is as follows:
• Max z= 5x₁-x₂-0×s₁-0×s₂
• Subject to the constraints:
  • x₁-3x₂+s₁ = 1
  • x₁-4x