Capital Co. is considering which of five 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 = 1,2,3,4,5. 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

Question

Quizplus · Accepted Answer

The objective function should maximize the net present value (NPV) of the projects. Therefore, we should choose the option that maximizes the sum of the NPV for each project that is selected. Option D maximizes the sum of the NPV for each project by using the binary variables X_i to indicate which projects are selected.