Question 902359: A merchant plans to sell two models of compact disc players at costs of $250 and $400. The $250 models yields a profit of $45, and the $400 model yields a profit of $50. He merchant estimates that the total monthly demand will not exceed 250 units. The merchant does not want to invest more than $70,000 in inventory for these products. Find the number of units of each model that should be stocked in order to maximize profit.
So far I have the constraints
P=250x+400x<=70,000
x+y<=250
x=>0
y=>0
Also how do I make this "The $250 models yields a profit of $45, and the $400 model yields a profit of $50" into an equation? Please show all your work I really need to understand this.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A merchant plans to sell two models of compact disc players at costs of $250 and $400.
The $250 models (x) yields a profit of $45, and the $400 model(y) yields a profit of $50.
The merchant estimates that the total monthly demand will not exceed 250 units. The merchant does not want to invest more than $70,000 in inventory for these products. Find the number of units of each model that should be stocked in order to maximize profit.
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How do I make this "The $250 models yields a profit of $45, and the $400 model yields a profit of $50" into an equation?
Objective function:: Profit = 45x + 50y
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So far I have the constraints
Cost = 250x+400y <= 70,000
x+y<=250
x=>0
y=>0
Please show all your work
Solve constraints for "y" and graph them::
y <= (-5/8)x + 175
y <= -x + 250
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Find the intersection of these two constraints::
(-5/8)x+175 = -x+250
(3/8)x = 75
x = 75/(3/8) = 200
Then y = -200+250 = 50
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Comment:: Evaluate the objective function with each of
the coordinate pairs of the corners of the inclosed area.
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Choose the (x,y) values that maximize the Profit.
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Cheers,
Stan H.
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