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 8 min of labor. To produce each model B grate requires 5 lb of cast iron and 5 min of labor. The profit for each model A grate is $2.00, and the profit for each model B grate is $1.50. If 900 lb of cast iron and 900 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 =      subject to the constraints cast iron labor x 0 y 0

Explanation / Answer

given Kane Manufacturing has a division that produces two models of fireplace grates,

x units of model A and

y units of model B.

maximize p=2x+1.5y

subject to

3x+5y<=900 .......(cast iron constraints)

8x+5y<=900 .........(labour constarints)

x>=0,

y 0

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