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:

Canada

A country in North America known for its vast landscapes, multicultural cities, and as a member of the Commonwealth with a system of parliamentary democracy.

Middle Management Positions

Roles within an organization that are primarily responsible for executing the policies and plans of senior management and overseeing the work of junior staff.

Gender Differences

Variations in characteristics, behaviors, and roles traditionally associated with being male or female in a given culture.

Ratings Of Effectiveness

Evaluations or assessments of how well an individual, system, or process achieves its intended goals or outcomes.