A Manufacturer Wants to Construct Warehouses in Six Different Locations

question 33

Essay

A manufacturer wants to construct warehouses in six different locations of the city to supply dry cells to his customers on time. The manufacturer wants to construct the minimum number of warehouses such that each warehouse is within 40 miles of at least one other warehouse. The following table provides the distance (in miles) between the locations. $$\begin{array} { l c c c c c c } &&& { \text { To } } \\\hline \text { From } & \text { Location A} & \text { Location B } & \text {Location C } & \text { Location D } & \text { Location } \mathrm { E } & \text { Location } \mathrm { F } \\\hline \text { Location A } & 0 & 35 & 40 & 45 & 60 & 70 \\\text { Location B } &&0&35&40&70&75\\\text { Location C } & & &0&45&50&50\\\text { Location D } & & && 0&40&50\\\text { Location E } & & &&& 0 & 30& \\\text { Location F } & & & &&& 0\end{array}$$ Formulate and solve an integer linear program that can be used to determine the minimum number of warehouses needed to be constructed. What are their locations?

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Definitions:

Pure Monopoly

A market structure where a single supplier controls all production and sale of a particular good or service, with no close substitutes.

Output Quantity

The total amount of a product or service produced by a company or industry.

Rent-seeking

The practice of gaining economic advantage by manipulating the social or political environment in which economic activities occur, instead of by creating new wealth.

Patent Protection

A legal right granted by the government to an inventor, giving them the exclusive right to make, use, or sell their invention for a certain period.