Formulate but do not solve the following exercise as a linear programming problem. Kane Manufacturing has a division that produces two models of fireplace grates, x units of model A and y units of model B. To produce each model A requires 3 lb of cast iron and 6 min of labor. To produce each model B grate requires 4 lb of cast iron and 5 min of labor. The profit for each model A grate is $1.50, and the profit for each model B grate is $1.00. If 1100 lb of cast iron and 1200 min of labor are available for the production of grates per day, how many grates of each model should the division produce per day to maximize Kane's profits P in dollars?

Maximize		P	=	1.50x+1.00y	subject to the constraints
cast iron				3x+4y1100
labor
				x 0
				y 0

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Formulate but do not solve the following exercise as a linear programming problem. National Business Machines manufactures x model A fax machines and y model B fax machines. Each model A cost $110 to make, and each model B costs $140. The profits are $35 for each model A and $35 for each model B fax machine. If the total number of fax machines demanded per month does not exceed 2100 and the company has earmarked not more than $600,000/month for manufacturing costs, how many units of each model should National make each month to maximize its monthly profits P in dollars?

Maximize		P	=	35x+35y	subject to the constraints
manufacturing costs				110x+140y600,000
number produced
				x 0
				y 0