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Question 504627: 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 7 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 $1.50, and the profit for each model B grate is $2.40. If 920 lb of cast iron and 1620 min of labor are available for the production of grates per day, how many grates of each model should the division produce per day in order to maximize Kane's profits P?
P = ? subject to the constraints
cast iron ?
labor ?
x ≥ 0
y ≥ 0
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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 7 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 $1.50, and the profit for each model B grate is $2.40.
If 920 lb of cast iron and 1620 min of labor are available for the production of grates per day, how many grates of each model should the division produce per day in order to maximize Kane's profits P?
:
The amt of cast iron constraint
2x + 4y =< 920
the labor constraint
7x + 4y =< 1620
:
You can solve this by elimination, multiply those x,y values by profit on each
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