A farmer in Wood County has 950 acres of land. She is going to plant each acre w

Question

A farmer in Wood County has 950 acres of land. She is going to plant each acre with com. soybeans, or wheat Each acre planted with com yields a $2,200 profit; each with soybeans yields $2,450 profit; and each with wheat yields $3,150 profit. She has 192 workers and 195 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 com. 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.)

Explanation / Answer

Linear Programming Equations

Let the acres used in corn , soyabean and wheat be x,y and z respectively.

We get

x = 890 , y = 50 and z = 10

So , Profit

Profit Function 2200x 2450y 3150z Subject to x y z =950 0.2x 0.2y 0.4z =192 0.2x 0.3y 0.2z =195

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