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:

Anhidrosis

The incapacity for normal perspiration, potentially causing the body to overheat.

Sweat

A liquid produced by the body's sweat glands designed to cool the body through evaporation, also known as perspiration.

Dermis

The thick layer of living tissue below the epidermis containing hair follicles, sweat glands, and providing mechanical strength to the skin.

True Skin

Another term for the dermis, the layer of skin located beneath the epidermis, containing nerve endings, sweat glands, and blood vessels.