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Question 608541: A manufacturer makes two types of jet skis, regular and deluxe. The profit on the regular jet ski is $200 and the profit on the delux is $250. To meet customer demand the company must make at least 50 regular and 75 delux models per week. To maintain high quality they must not exceed more than 150 jet skis per week. How many jet skis of each type should be produced per week to obtain maximum profit? What is the maximum weekly profit?
Trying to graph and solve using objective function to no avail. Thank you for your help.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A manufacturer makes two types of jet skis, regular and deluxe. The profit on the regular jet ski is $200 and the profit on the delux is $250. To meet customer demand the company must make at least 50 regular and 75 delux models per week. To maintain high quality they must not exceed more than 150 jet skis per week. How many jet skis of each type should be produced per week to obtain maximum profit? What is the maximum weekly profit
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Equations:
r + d <= 150
r >= 50
d >= 75
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Graph:
r = -d+150 and shade the area below it in the 1st Quadrant:
Graph:
r = 50 as a horizontal line; shade the area above it but below
r = -d+150
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d = 75 as a vertical line; shade the area to the right of it
but below r = -d+150
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Objective Funct: Profit = 200r + 250d
Find the vertex points of the enclosed shaded area:
If d = 75, r = 75 giving you (75,75) and profit = 75(200+250) = 33750
If r = 50, d = 100 giving you (100,50) and profit = 100*200+50*250 = 32500
If d = 75, r = 50 giving you(75,50) and profit = 75*200 + 50*250 = 27500
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Cheers,
Stan H.
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