Hello, I am having trouble finding how to solve for Model A. Thank you:) Questio

Question

Hello, I am having trouble finding how to solve for Model A. Thank you:)

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 2 lb of cast iron and 8 min of labor. To produce each model B grate requires 4 lb of cast iron and 4 min of labor. The profit for each model A grate is $2.50, and the profit for each model B grate is $2.00. 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?

Explanation / Answer

Maximize Profit, p = 2.5x + 2y

subject to the constraints

2lb cast iron required model A and 4lb cast iron required for model B and maximum iron available is 1200lb
cast iron: 2x + 4y <= 1200

8mins labor is required for model A and 4 mins labor is required for model B and maximum labor available is 900min
labor: 8x + 4y <= 900

minimum 150 units of model A need to be produced
Model A: x >= 150

y>= 0

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