SOLUTION: A small company produces both doll houses and sets of doll furniture. The doll houses take 3 hours of labor to produce, and the furniture sets take 8 hours. The labor available i
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Question 94522: A small company produces both doll houses and sets of doll furniture. The doll houses take 3 hours of labor to produce, and the furniture sets take 8 hours. The labor available is limited to 400 hours per week, and the total production capacity is 100 items per week. Existing orders require that at least 20 doll houses and 10 sets of furniture be produced per week. Write a system of inequalities representing this situation, where x is the number of doll houses and y is the number of furniture sets. Then graph the system of inequalities Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! A small company produces both doll houses and sets of doll furniture.
Let the number of houses be "h" and the number of furnitures be "f"
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The doll houses take 3 hours of labor to produce, and the furniture sets take 8 hours.
The labor available is limited to 400 hours per week, and the total production capacity is 100 items per week.
Labor inequality: 3h+8f<=400
Production inequality: h+f<=100
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Existing orders require that at least 20 doll houses and 10 sets of furniture be produced per week.
h>=20
f>=10
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Write a system of inequalities representing this situation, where h is the number of doll houses and f is the number of furniture sets.
Solve each inequality for f as follows:
Labor: f(h) = -(3/8)h+50
Production: f(h)<=-h+100
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Then graph the system of inequalities
Label the horizontal axis as "h"; Label the vertical axis as "f"
Draw a vertical line at h=20
Draw a horizontal line at f=10
Comment: Remember solutions are restricted to f>=10 and h>=20
Comment: I can't shade the proper inequality areas on this site.
Hopefully you can do that.
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Cheers,
Stan H.
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