Chapter 16.5, Problem 56PS

Solve the linear programming problems in Problems 56 – 59.

Suppose the net profit per bushel of corn in Example 3 increased to $2.00 and the net profit per bushel of wheat dropped to $1.50. Maximize the profit if the other conditions in the example remain the same.

Example 3:

A farmer has 100 acres on which to plant two crops, corn and wheat, and the problem is to maximize the profit. There are several considerations; the first is the expense:

	Cost per Acre
Expenses	Corn	Wheat
Seed	$12	$40
Fertilizer	$58	$80
Planting/care/harvesting	$50	$90
Total	$120	$210

After the harvest, the farmer must store the crops while awaiting proper market conditions. Each acre yields an average of 110 bushels of corn or 30 bushels of wheat. The limitations of resources are as follows:

Available capital: $15000

Available storage facilities: 4000 bushels

If the net profit (after all expenses have been subtracted) per bushel of corn is $1.30 and for wheat is $2.00, how should the farmer plant the 100 acres to maximize the profits?