Riker Co Is Considering Which of 4 Different Projects to Undertake

Multiple Choice

Riker Co. is considering which of 4 different projects to undertake in order to maximize its net present value (NPV) . Define X_i as a binary 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. 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