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:

Setup Costs

The expenses incurred to ready equipment, processes, or systems for production or operation. These costs do not vary with the quantity produced.

Order Cycles

The process or sequence of events from placing an order to receiving goods, often part of inventory management strategies.

Carrying Cost

The total cost of holding inventory, including storage, maintenance, and insurance.

Ordering Cost

The expenses incurred in placing and processing orders to suppliers.