Capital Co

question 116

Multiple Choice

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
Which of the following represents the constraint stating that project 1 can be undertaken only if project 5 is undertaken?

• A) X₁ + X₅ ≤ 1
• B) X₁ - X₅ ≤ 0
• C) X₅ - X₁ ≤ 0
• D) X₁ - X₅ ≤ 1
• E) X₅ - X₁ ≤ 1

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Definitions:

Total Variable Cost

The sum of all costs that vary with the level of output, including things like raw materials, labor costs that vary with production volume.

Output Increases

A situation where a firm or economy produces a greater quantity of goods or services.

Total Variable Cost

The sum of expenses that vary directly with the level of production output, excluding any fixed costs.

Marginal Cost

The additional cost incurred from producing one more unit of a product or service.