A Company Wants to Build a New Factory in Either

question 24

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.
$$\begin{array} { c l c c } \text { Variable } & \text { Decision } & \begin{array} { c } \text { NPV } \\\text {( \$ millon )}\end{array} & \begin{array} { c } \text { Cost } \\\text {( \$ millon )} \end{array} \\\hline \mathbf { X } _ { 1 } & \text { Factory in Columbia } & 3 & 10 \\\mathbf { X } _ { \mathbf { 2 } } & \text { Factory in Atlanta } & 4 & 8 \\\mathbf { X } _ { 3 } & \text { Warehouse in Columbia } & 2 & 6 \\\mathbf { X } _ { 4 } & \text { Warehouse in Atlanta } & 1 & 5\end{array}$$ Based on this ILP formulation of the problem what is the optimal solution to the problem?
$\begin{array} { l l } \text { MAX: } & 3 \mathbf { X } _ { 1 } + 4 \mathbf { X } _ { \mathbf { 2 } } + 2 \mathbf { X } _ { \mathbf { 3 } } + \mathbf { X } _ { 4 } \\ \text { Subject to: } & 10 \mathbf { X } _ { 1 } + \mathbf { 8 } \mathbf { X } _ { \mathbf { 2 } } + 6 \mathbf { X } _ { \mathbf { 3 } } + 5 \mathbf { X } _ { \mathbf { 4 } } \leq 15 \\ & \mathbf { X } _ { 1 } + \mathbf { X } _ { \mathbf { 2 } } = 1 \\ & \mathbf { X } _ { \mathbf { 3 } } + \mathbf { X } _ { \mathbf { 4 } } \leq 1 \\ & \mathbf { X } _ { \mathbf { 3 } } - \mathbf { X } _ { 1 } \leq 0 \\ & \mathbf { X } _ { \mathbf { 4 } } - \mathbf { X } _ { \mathbf { 2 } } \leq 0 \\ & \mathbf { X } _ { \mathrm { i } } = 0,1 \end{array}$

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Definitions:

Concentration Ratio

An indicator used to measure the degree of market concentration, often defined by the market share of the largest firms within an industry.

Cut-Throat Competitor

A company or individual that employs aggressive and ruthless tactics to maintain or increase its market position.

Colluder

An entity that engages in collusion, cooperating with others secretly or illegally to deceive or defraud.

Degree Of Oligopolization

The extent to which a market or industry is dominated by a few large companies, limiting competition.