A Company Wants to Build a New Factory in Either

question 74

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 $16 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 formulas should go in cells F6:F14 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:

Legal Offer

A proposal by one party to another intended to create a legally binding agreement upon acceptance.

Transformation Processes

The operations or activities that convert inputs into outputs, adding value in manufacturing or service provision.

Operations Management

The administration of business practices to create the highest level of efficiency possible within an organization.

Quality

How well a good or service meets or exceeds customers’ expectations, or the degree to which a product conforms to established tolerance standards.