Question 162545: The Slip and Slide Ski Company manufactures downhill skis and cross country skis. A pair of downhill skis requires 2 man-hours for cutting, 1 man-hour for shaping, and 3 man-hours for finishing while a pair of cross country skis requires 2 man-hours for cutting, 2 man-hours for shaping, and 1 man-hour for finishing. Each day the company has available 140 man-hours for cutting, 120 man-hours for shaping, and 150 man-hours for finishing. How many pairs of each type of ski should the company produce to maximize their profit if a pair of downhil yields a profit of $10 and a pair of cross country skis yields a profit of $8?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The Slip and Slide Ski Company manufactures downhill skis and cross country skis.
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A pair of downhill skis requires 2 man-hours for cutting, 1 man-hour for shaping, and 3 man-hours for finishing;
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a pair of cross country skis requires 2 man-hours for cutting, 2 man-hours for shaping, and 1 man-hour for finishing.
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Each day the company has available 140 man-hours for cutting, 120 man-hours for shaping, and 150 man-hours for finishing.
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Cutting Inequality: 2d + 2c <= 140
Shaping Inequality: 1d + 2c <= 120
Finishg Inequality: 3d + 1c <= 150
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How many pairs of each type of ski should the company produce to maximize their profit if a pair of downhill yields a profit of $10 and a pair of cross country skis yields a profit of $8?
Total profit = 10d + 8c
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Let "c" be the dependent variable and "d" be the independent variable:
c >= 0
d >= 0
c <= -d + 70
c <= -(1/2)d + 60
c <= -3d + 150
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Graph the three inequalities and note the coordinates of the vertices in
the 1st Quadrant:
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I'm going to assume you know you need to find the coordinates of the
intersection of each pair of equations. You get these coordinate pairs:
P = 10d + 8c
(0,60) has a P value of 480
(50,0) has a P value of 500
(20,50) has a P value of 600
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Ans: Maximum Profit if c=50 and d=20
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Comment: I recommend you check the arithmetic carefully.
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Cheers,
Stan H.
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