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:

Conversion Costs

The total expense required to convert raw materials into finished goods, including labor and overhead costs.

Process Costing

An accounting methodology that traces and accumulates direct costs, and allocates indirect costs of a manufacturing process, to calculate the total cost of manufacturing a product.

Weighted-Average Method

An inventory costing method that calculates the cost of goods sold and ending inventory based on the average cost of all goods available for sale during the period.

Conversion Costs

The sum of direct labor and manufacturing overhead costs, representing the costs incurred to convert raw materials into finished goods.