A Company Wants to Build a New Factory in Either

question 21

Essay

A company wants to build a new factory in either Atlanta or Columbia.It is also considering building a warehouse in whichever city is selected for the new factory.The following table shows the net present value NPV)and cost of each facility.The company wants to maximize the net present value of its facilities,but it only has $15 million to invest.
Variable Decision
NPV
$million)
Cost $million)
^X₁ Factory in Columbia 3 10
^X₂ Factory in Atlanta 4 8
^X₃ Warehouse in Columbia 2 6
^X₄ Warehouse in Atlanta 1 5
Based on this ILP formulation of the problem and the indicated optimal solution what values should go in cells B6:G14 of the following Excel spreadsheet?
MAX: ^{3 X}₁ ^{+ 4 X}₂ ^{+ 2 X}₃ ^{+ X}₄
Subject to: ^{10 X}₁ ^{+ 8 X}₂ ^{+ 6 X}₃ ^{+ 5 X}₄ ^{≤ 15}
X₁ + X₂ = 1 X₃ + X₄ ≤ 1 X₃ − X₁ ≤ 0 X₄ − X₂ ≤ 0
X_i = 0,1

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Definitions:

Surplus

The amount by which production or supply exceeds demand or usage.

Production Sites

Locations where goods are manufactured or assembled, characterized by the presence of facilities and machinery for production.

Storage Sites

Locations or facilities used for the safekeeping of goods or materials until they are needed or dispatched.

Return On Equity (ROE)

A measure of a corporation's profitability that reveals how much profit a company generates with the money shareholders have invested.