A farmer in Wood County has 880 acres of land. She is going to plant each acre w

Question

A farmer in Wood County has 880 acres of land. She is going to plant each acre with corn, soybeans, or wheat. Each acre planted with corn yields a $1,900 profit; each with soybeans yields $2,700 profit; and each with wheat yields $2,950 profit. She has 241 workers and 113 tons of fertilizer. The table below shows the requirement per acre of each of the crops CORN SOYBEANS WHEAT Labor (workers) 0.3 Fertilizer (tons) 0.1 0.2 0.3 0.4 Assuming a linear relationship, use 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. (However, round the final values of these decision variables to the nearest whole number when entering those answers. Use these rounded decision variable values to compute "Total Profit" and enter that answer to the nearest whole number. Lastly, also use the rounded decision variable values to compute the three "Resources Used" answers and enter them to the nearest whole number. Leave no cells blank-be certain to enter "O" wherever required.) Decision for corn Decision for soybeans Decision for wheat Total profit 1,900 2,700 2,950 Used Labor (workers) Fertilizer (tons) Acres Planted 241 0 113 880

Explanation / Answer

Let us define decision variables as C, S, and W representing the three crops corn, soybeans, and wheat respectively.

Formulation of the problem is as follows:

Solution using excel solver is as follows:

Integer values as per the question:

Formating the non integer cells as integers we get

Decision Variables Corn-C Soybeans-S Wheat-W SumProduct Values of D.V. Objective-Maximize Profit 1900 2700 2950 0 Sign RHS Constraint-Land 1 1 1 0 <= 880 Constraint-Labor 0.3 0.2 0.1 0 <= 241 Constraint-Fertilizer 0.1 0.3 0.4 0 <= 113

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