Formulate but do not solve the following exercise as a linear programming proble

Question

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 7 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. 1200 lb of cast iron and 900 min of labor are available for the production of grates per day. Because of a backlog of orders on model A grates, the manager of Kane Manufacturing has decided to produce at least 150 of these grates a day. Operating under this additional constraint, how many grates of each model should Kane produce to maximize profit P in dollars? Maximize P = subject to the constraints cast iron labor model A y 0

Explanation / Answer

Max Profit = 1.5 x+ 1*y
such That

3x + 4y <= 1200 (Cast Iron)

7x +5y <= 900 (Labor)

x>=150 (Model A)

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