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
What is the proper objective function?
a) Max X1 + X2 + X3 + X4 + X5
b) Min 60X1 + 50X2 + 40X3 + 20X4 + 30X5
c) Max 7X1 + 10X2 + 6X3 + 3X4 + 12X5
d) Max 60X1 + 50X2 + 40X3 + 20X4 + 30X5
e) Min 7X1 + 10X2 + 6X3 + 3X4 + 12X5
Answer: d