Appalachian Coal Company Must Mine a Minimum of 30 Tons

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. $\begin{array}{lccc}\text { Site } & \text { Weekly Operating } & \text { Mining Costs Per } & \text { Maximum Weekly } \\ &\text { Costs }\left(\$ 1000^{\prime} s\right) & \text { Ton }\left(\$ 1000^{\prime} s\right) & \text { Output (Tons) }\\\mathrm{A} & \$ 5 & \$ 12 & 10 \\\mathrm{~B} & \$ 6 & \$ 8 & 20 \\\mathrm{C} & \$ 2 & \$ 14 & 25 \\\mathrm{D} & \$ 7 & \$ 6 & 15\end{array}$