Question 102520
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.
{{{graph(400,300,-10,120,-10,120,10,100,(-3/8)x + 50,-x+100-x+100)}}}
 
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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.