Formulate but do not solve the following exercise as a linear programming problem. A company manufactures x units of Product A and y units of Product B, on two machines, I and II. It has been determined that the company will realize a profit of $3 on each unit of Product A and $5 on each unit of Product B. To manufacture a unit of Product A requires 6 min on Machine I and 4 min on Machine II. To manufacture a unit of Product B requires 9 min on Machine I and 5 min on Machine II. There are 351 min available on Machine I and 211 min available on Machine II in each work shift. How many units of a product should be produced in each shift to maximize the company's profit P in dollars?

Maximize		P	=		subject to the constraints
Machine I
Machine II
				x 0
				y 0

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

Formulate but do not solve the following exercise as a linear programming problem. A farmer uses two types of fertilizers. A 50-lb bag of Fertilizer A contains 8 lb of nitrogen, 2 lb of phosphorus, and 4 lb of potassium. A 50-lb bag of Fertilizer B contains 5 lb each of nitrogen, phosphorus, and potassium. The minimum requirements for a field are 440 lb of nitrogen, 260 lb of phosphorus, and 360 lb of potassium. If a 50-lb bag of Fertilizer A costs $50 and a 50-lb bag of Fertilizer B costs $20, find the amount of each type of fertilizer the farmer should use to minimize his cost C in dollars while still meeting the minimum requirements. (Let x represent the number of bags of Fertilizer A and y represent the number of bags of Fertilizer B.)

Minimize	C	=	subject to the constraints
nitrogen
phosphorus
potassium
			x 0
			y 0