A farmer in Wood County has 960 acres of land. She is going to plant each acre w

Question

A farmer in Wood County has 960 acres of land. She is going to plant each acre with corn, soybeans, or wheat. Each acre planted with corn yields a $2,300 profit; each with soybeans yields $2,400 profit; and each with wheat yields $3,100 profit. She has 196 workers and 126 tons of fertilizer. The table below shows the requirement per acre of each of the crops.

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 “0” wherever required.)

A farmer in Wood County has 960 acres of land. She is going to plant each acre with corn, soybeans, or wheat. Each acre planted with corn yields a $2,300 profit; each with soybeans yields $2,400 profit; and each with wheat yields $3,100 profit. She has 196 workers and 126 tons of fertilizer. The table below shows the requirement per acre of each of the crops.

Explanation / Answer

Corn planted in 745 acres

soyabeen planted in 130 acres

wheat planted in 85 acres

Total acres planted = 960

Total workers used = 196

Total fertilizers used = 126 tons

Total profit = $1713500 + $312000 + $263500 = $2289000

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