Two types of crops can be grown in particular irrigation area each year. Each unit quantity of crop A can be sold for a price PA and requires WA units of water, LA units of land, FA units of fertilizer, and HA units of labor. Similarly, crop B can be sold at a unit price of PB and requires WB, LB, FB and HB units of water, land, fertilizer, and labor, respectively, per unit of crop. Assume that the available quantities of water, land, fertilizer, and labor are known, and equal W, L, F, and H, respectively. (a) Structure a linear programming model for estimating the quantities of each of the two crops that should be produced in order to maximize total income.
(b) Solve the problem graphically, using the following data:
Resource Crop A Crop B Maximum Available Resources
Water 2 3 60
Land 5 2 80
Fertilizer 3 2 60
Labor 1 2 40
Unit Price 30 25