Capital Co. is considering which of five different projects to undertake in order to maximize its net present value (NPV). Define Xi 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?
a) X1 + X5 ≤ 1
b) X1 - X5 ≤ 0
c) X5 - X1 ≤ 0
d) X1 - X5 ≤ 1
e) X5 - X1 ≤ 1
Answer: b