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Question 61111: 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. 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.
0 solutions
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3x+8y<=400
x+y<=100
x>=20
y>=10
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Graph a vertical line at x=20 and a horizontal
line at y=10.
Shade the area that is above y=10 and to the right
of x=20.
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Graph the line y=-x+100
Shade the area below it that intersects the previous shaded area.
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Graph the line y=-(8/3)x+50
Shade the area below it that intersects both the previosly shaded areas.
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Cheers,
Stan H.
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