Riker Co Is Considering Which of Four Different Projects to Undertake

Multiple Choice

Riker Co. is considering which of four 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. 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