Consider the following constraint that needs to be expressed as a goal:
3X₁ + 4X₂ ≤ 11.
The correct format is:
A)3X₁ + 4X₂ - d₁⁻ + d₁⁺ = 11
B)3X₁ + 4X₂ + d₁⁻ - d₁⁺ = 11
C)3X₁ + 4X₂ + d₁⁻ - d₁⁺ ≥ 11
D)3X₁ + 4X₂ + d₁⁻ - d₁⁺ ≤ 11
E)3X₁ + 4X₂ + d₁⁻ - d₁⁺ ≠ 11

Question

Quizplus · Accepted Answer

The correct format for expressing the constraint 3X₁ + 4X₂ ≤ 11 as a goal is to add slack variables (d₁⁻ for underachievement and d₁⁺ for overachievement) to the equation. The correct way to do this while maintaining the original inequality's direction (≤) is to add the slack variable that compensates for the inequality (d₁⁻) and subtract the surplus variable (d₁⁺), resulting in the equation 3X₁ + 4X₂ + d₁⁻ - d₁⁺ = 11. This allows the equation to be flexible for both under and overachievement relative to the target value of 11, while originally aiming not to exceed it.

Consider the Following Constraint That Needs to Be Expressed as a Goal