A Farmer Is Planning His Spring Planting Formulate the LP for This Problem

Essay

A farmer is planning his spring planting. He has 20 acres on which he can plant a combination of Corn, Pumpkins and Beans. He wants to maximize his profit but there is a limited demand for each crop. Each crop also requires fertilizer and irrigation water which are in short supply. There are only 50 acre ft of irrigation available and only 8,000 pounds/acre of fertilizer available. The following table summarizes the data for the problem.
$$\begin{array} { l | c c c c c } \text { Crop } & \begin{array} { c } \text { Profit per } \\\text { Acre } ( \$ )\end{array} & \begin{array} { c } \text { Yield per } \\\text { Acre (Ib) }\end{array} & \begin{array} { c } \text { Maximum } \\\text { Demand (Ib) }\end{array} & \begin{array} { c } \text { Irrigation } \\\text { (acre ft) }\end{array} & \begin{array} { c } \text { Fertilizer } \\\text { (pounds/acre) }\end{array} \\\hline \text { Corn } & 2,100 & 21,000 & 200,000 & 2 & 500 \\\text { Pumpkin } & 900 & 10,000 & 180,000 & 3 & 400 \\\text { Beans } & 1,050 & 3,500 & 80,000 & 1 & 300\end{array}$$ Formulate the LP for this problem.