Expert: Richard J. Raridon - 4/23/2007

Question
Hi Richard, I have another pesky word problrm I can't figure out. We are doing linear programming so I know I need to set up a system of equations for this problem but I can't figure out the equations for the life of me. Here is the problem.

Use linear programming to solve the following problem.

Farmer Brown is planning his planting for the coming year. He expects to raise two crops: potatoes and wheat. He has 100 acres of land available for planting and will be able to devote 160 days of labor to his crops. He expects an acre of wheat to require 4 days of labor while an acre of potatoes requires only one day.

He has $1,100 that he can use for the start-up costs of planting and cultivating. It costs $10 an acre to plant and cultivate potatoes, while the corresponding costs for an acre of wheat are $20.

If Brown expects a revenue of $40 per acre for potatoes and $120 an acre for wheat, how many acres of each should he plant in order to achieve the maximum possible revenue?  

Answer
It looks like you have conflicting data.  If P = acres of potatoes and W = acres of wheat, then
P+W = 100 and 4W+P = 160 which leads to P=80 and W=20
However, you also have 10P+20W = 1100 which doesn't fit.
Since he will clear $30 per acre on potatoes and $100 per acre on wheat, R(evenue) = 30P +100W