Mathematical Linear Programming Question?

Question

I’m stuck on this linear programming math problem. If you could please help point me in the right direction, I would appreciate it.


A farmer has 20 days in which to plant corn and soybeans. The corn can be planted at a rate of 10 acres per day and the soybeans at a rate of 15 acres per day. The farm has 250 acres available for planting. If the profit of corn is $30 per acre, and the profit on soybeans is $25 per acre, how many of each should the farmer plant to maximize profit?

Answer 1

Here's how you can set it up:

Maximize: Profit = 30 C + 25 B

Subject to: 20 >= C/10 + B/15 (the time constraint)

Subject to: 250 = C + B (the acreage constraint)

If you graph the constraints on graph paper, with C as a function of B, the optimum is at one of the "corners", that is either B = 250, C = 0; B = 0, C = 200; or the point where the two functions lines cross.

Find the point of crossing by solving both constraints for C, make them equal and solve for B.

Plug the possible points into your objective equation, and pick the highest profit.