Capital Co. is considering five different projects. Define X_i as a binary (0-1) variable that equals 1 if project i is undertaken and 0 otherwise, for i = 1,2,3,4,5. Which of the following represents the constraint(s) stating that projects 2, 3, and 4 cannot all be undertaken simultaneously? A) X₂ + X₃ + X₄ ≤ 3 B) X₁ + X₂ + X₃ + X₄ + X₅ ≤ 3 C) X₂ + X₃ + X₄ ≤ 1 D) X₂ + X₃ + X₄ ≤ 2 E) X₂ + X₃ ≤ 1 and X₃ + X₄ ≤ 1

Question

Quizplus · Accepted Answer

The correct constraint to ensure that projects 2, 3, and 4 cannot all be undertaken simultaneously is to limit the sum of their binary decision variables to be less than or equal to 2. This allows any two of the projects to be selected but not all three at the same time.