Capital Co. is considering which of five different projects to undertake in order to maximize its net present value (NPV) . 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. The NPV and required capital (in thousands) for each project are listed below.
Project Net Present Value Capital Required
1 60 7
2 50 10
3 40 6
4 20 3
5 30 12
Which of the following represents the constraint stating that project 1 can be undertaken only if project 5 is undertaken?

Question

Quizplus · Accepted Answer

This constraint ensures that if project 1 is selected (X₁ = 1), then project 5 must also be selected (X₅ = 1), making the statement true (0 ≤ 0). If project 1 is not selected but project 5 is, the inequality still holds (−1 ≤ 0). This effectively enforces the condition that project 1 can only proceed if project 5 does.