A farmer has 360 acres of land on which to plant corn and wheat. She has...

A farmer has 360 acres of land on which to plant corn and wheat. She has $24,000 in resources to use for planting and tending the fields and storage facility sufficient to hold 18,000 bushels of the grain (in any combination). From past experience, she knows that it costs $120 / acre to grow corn and $60 / acre to grow wheat; also, the yield for the grain is 100 bushels / acre for corn and 40 bushels / acre for wheat. If the market price is $225 per acre for corn and $100 per acre for wheat, how many acres of each crop should she plant in order to maximize her revenue?

1. Set up a linear programming problem, choosing variables, finding a formula for your objective function, and inequalities to represent the constraints.

2. You will need to decide a reasonable range for your variables, and then put in a column of values within that range for the x-variable in column A. Then you want to solve each constraint equation for y, and use that formula to get values in the "y for C1", etc., columns (B, C, D). Then graph the three constraint lines on one graph (as you did in Lab 1: open its Word document if you need refreshing on how to do this).

3. Shade in the feasible region.

4. Find the corners of the feasible region using goal seek to find intersections of lines, as you did in Lab 1.

5. Find in column H the values of f at the corners of the feasible region.

6. Determine the maximum revenue.

7. Finally, using new objective functions for when the prices of corn are at their highs and lows, answer the final question. This only involves computing new values of the objective function, not any new graphing or constraints.

x represents:

y represents:

Formula for objective function: f =

Constraint 1:

Constraint 2:

Constraint 3:

Corners of feasible region f at corners

So how many acres of each crop should she plant?

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Expert Solution

milcah answered 1 year ago

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