Riker Co Is Considering Which of Four Different Projects to Undertake

question 11

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

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Definitions:

Direct Labor Cost

The total expense of paying for the labor of employees directly involved in manufacturing a product or delivering a service.

Budgeted Direct Labor Cost

The estimated cost of labor directly involved in the production process, as planned in the budget.

Labor Rate Variance

The difference between the actual cost of direct labor and the estimated cost, indicating how well labor costs were controlled.

Direct Labor-hours

The complete tally of hours that workers, directly involved in making products or providing services, spend working.