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 thefields and storage facility sufficient to hold 18,000 bushels ofthe grain (in any combination). From past experience, she knowsthat it costs $120 / acre to grow corn and $60 / acre to growwheat; also, the yield for the grain is 100 bushels / acre for cornand 40 bushels / acre for wheat. If the market price is $225 peracre for corn and $100 per acre for wheat, how many acres of eachcrop should she plant in order to maximize her revenue?

A.

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

2. You will need to decide a reasonable range for yourvariables, and then put in a column of values within that range forthe x-variable in column A. Then you want to solve each constraintequation for y, and use that formula to get values in the "y forC1", etc., columns (B, C, D). Then graph the three constraint lineson one graph (as you did in Lab 1: open its Word document if youneed refreshing on how to do this).

3. Shade in the feasible region.

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

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

6. Determine the maximum revenue.

7. Finally, using new objective functions for when the prices ofcorn are at their highs and lows, answer the final question. Thisonly involves computing new values of the objective function, notany new graphing or constraints.

x represents:

y represents:

Formula for objective function: f =

Constraint 1:

Constraint 2:

Constraint 3:

Corners of feasibleregion          f at corners

So how many acres of each crop should she plant?