A Snack Food Producer Runs Four Different Plants That Supply

Essay

A snack food producer runs four different plants that supply product to four different regional distribution centers.The division operations manager is focused on one product,so he creates a table showing each plant's monthly capacity and each distribution center's monthly demand (both amounts in cases)for the product.The division manager supplements this table with the cost data to ship one case from each plant to each distribution center.Formulate an objective function and constraints that will solve this problem using linear programming.
$$\begin{array} { | c | l | l | l | l | l | } \hline & \text { Center 1 } & \text { Center 2 } & \text { Center 3 } & \text { Center 4 } & \begin{array} { l } \text { Monthly } \\\text { Capacity }\end{array} \\\hline \text { Plant A } & \$ 2 & \$ 7 & \$ 5 & \$ 4 & 8000 \\\hline \text { Plant B } & \$ 9 & \$ 4 & \$ 7 & \$ 6 & 12000 \\\hline \text { Plant C } & \$ 7 & \$ 6 & \$ 4 & \$ 3 & 7500 \\\hline \text { Plant D } & \$ 4 & \$ 8 & \$ 3 & \$ 5 & 5000 \\\hline \begin{array} { l } \text { Monthly } \\\text { Demand }\end{array} & 9000 & 8500 & 8000 & 7000 & \\\hline\end{array}$$