Operations Management

Question 8

Please show work and explain. Thank you..

A farmer in Wood County has 1,090 acres of land. She is going to plant each acre with corn, soybeans, or wheat. Each acre planted with corn yields a $1,600 profit; each with soybeans yields $3,100 profit; and each with wheat yields $1,600 profit. She has 355 workers and 485 tons of fertilizer. The table below shows the requirement per acre of each of the crops.

Assuming a linear relationship, use the Excel Solver to determine the optimal planting mix of corn, soybeans, and wheat to maximize her profits. In formulating your linear program, do NOT restrict the three decision variables to integer values. (Round the final values of the decision variables to the nearest whole number. Use these rounded values to compute all subsequent answers and enter each of those answers as whole numbers. Leave no cells blank be certain to enter 0 wherever required.)

Labor(workers)Fertilizer(tons)CORN0.50.7SOYBEANS0.60.3WHEAT0.30.3 \begin{tabular}{|l|l|} \hline & \\ \hline Decision for corn acres planted & \\ \hline Decision for soybeans acres planted & \\ \hline Decision for wheat acres planted & \\ \hline Total profit & \\ \hline \end{tabular} \begin{tabular}{|l|l|} \hline & Resources Used \\ \hline Labor (workers) & \\ \hline Fertilizer (tons) & \\ \hline Acres Planted & \\ \hline \end{tabular}