A Company Wants to Build a New Factory in Either

question 10

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.
Formulate the ILP for this problem.
$$\begin{array} { c l c c } \text { Variable } & \text { Decision } & \begin{array} { c } \text { NPV } \\\text { (\$million) }\end{array} & \begin{array} { c } \text { Cost } \\\text {( \$ millon )}\end{array} \\\hline \mathbf { X } _ { 1 } & \text { Factory in Columbia } & 3 & 10 \\\mathbf { X } _ { \mathbf { 2 } } & \text { Factory in Atlanta } & 4 & 8 \\\mathbf { X } _ { 3 } & \text { Warehouse in Columbia } & 2 &6\\\mathbf { X } _ { 4 } & \text { Warehouse in Atlanta } & 1 & 5\end{array}$$

---

Definitions:

Competitive Price-Taker

An entity in a market that has no control over the prices at which its products are sold, typically due to intense competition and product uniformity.

Marginal Cost

The cost of producing one additional unit of a product.

Average Total Cost

The total cost of production divided by the quantity of output produced, representing the cost per unit of output.

Profit

The financial gain made in a transaction or the operation of a business after subtracting all expenses.