Problem
A farmer has subdivided his land into three plots and wants to plant three crops in each plot: corn, rice, and soy. Plot sizes, crop acreage, profit per acre, and manure needed (pounds per acre) are given in the table at the bottom of this page. The maximum acreage for each crop denotes the total acres of that crop that can be planted over all three plots. Currently there are 450,000 pounds of manure available. To ensure that the plots are used equitably, the farmer wants the same proportion of each plot to be under cultivation. (The proportion of each plot under cultivation must be the same for all three plots.) How much of each crop should be planted at each plot to maximize total profit?
