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

Question 102520: 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.
PLEASE help me with this again I am soo terribel with wrod problems like this.
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 x is the number of doll houses and y is the number of furniture sets.
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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 Equation: 3x+8y<= 400
Production equation: x+y <=100
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Solve each for y; needed for graphing later
y <= (-3/8)x + 50
y <= -x+100
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Existing orders require that at least 20 doll houses and 10 sets of furniture be produced per week.
x>=20
y>=10
Write a system of inequalities
Then graph the system of inequalities.

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On an x/y coordinate system:
Draw a vertical line at x = 20 and at x=100
Draw a vertical line at y = 10 and at y=100
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Comment
The resulting box limits the domain and the range.
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Graph the Labor and the Production inequalities in the box.
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Cheers,
Stan H.

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