Riker Co. is considering which of four 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. The NPV and required capital (in millions) for each project are listed below.
Project Net Present Value Capital Required
1 60 7
2 50 10
3 40 6
4 20 3
Which of the following represents the constraint(s) stating that project 1 must be undertaken and at least one of the other projects must be undertaken?
a) X1 + X2 ≤ 1, and X1 + X3 ≤ 1, and X1 + X4 ≤ 1
b) X1 ≥ 1, and X2 + X3 + X4 ≥ 1
c) X1 + X2 ≥ 1, and X1 + X3 ≥ 1, and X1 + X4 ≥ 1
d) X1 ≥ 1, and X2 + X3 + X4 ≤ 3
e) X1 + X2 + X3 + X4 ≥ 2
Answer: b