Appalachian Coal Company Must Mine a Minimum of 30 Tons

question 2

Essay

Appalachian Coal Company must mine a minimum of 30 tons of coal weekly.It can mine at any of four sites.Relevant data concerning fixed weekly operation costs of the sites, variable mining costs per ton of coal, and estimated maximum weekly output of coal at each site are given in the following table.Formulate a mixed integer programming model and solve for the mining strategy that will minimize total weekly costs. $\begin{array}{lccc}\text { Site } & \text { Weekly Operating } & \text { Mining Costs Per } & \text { Maximum Weekly } \\ &\text { Costs }\left(\$ 1000^{\prime} s\right) & \text { Ton }\left(\$ 1000^{\prime} s\right) & \text { Output (Tons) }\\\mathrm{A} & \$ 5 & \$ 12 & 10 \\\mathrm{~B} & \$ 6 & \$ 8 & 20 \\\mathrm{C} & \$ 2 & \$ 14 & 25 \\\mathrm{D} & \$ 7 & \$ 6 & 15\end{array}$

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Definitions:

Axillary Lymph Nodes

Lymph nodes located in the armpit (axilla) that play a key role in filtering lymph fluid and fighting infection.

Right Lymphatic Duct

A lymphatic vessel that drains lymph from the right upper limb, right side of the thorax, and right sides of the head and neck.

Right Lymphatic Duct

A vessel in the lymphatic system that drains lymph from the right upper limb, right side of the thorax, and right halves of the head and neck.

Brachiocephalic

Refers to the vein or artery that supplies blood to the arms and the head, particularly prominent in the circulatory system.