Question 316412
A small company produces both doll houses and sets of doll furniture. 
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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.
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Quantity Inequality: x + y <= 100
Labor Inequality::: 3x +8y <= 400 hrs
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Existing orders require that at least 20 doll houses and 10 sets of furniture be produced per week. 
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x >= 20
y >= 10
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Solve for x and y, where x is the number of doll houses and y is the number of furniture sets that can be produced to optimize the operation.
Quantity: y <= 100-x
Labor::: y <= (-3/8)x + 50
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{{{graph(400,300,-10,120,-10,120,(-3/8)x+50,100-x,10)}}}
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Also: Draw a vertical line at x = 20
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Can you take it from here?
Cheers,
Stan H.

 [Hint: Set up system of linear inequalities and find the intersection of the two items). Put your answer in the form of (x,y), where x is the number of doll houses to be produced and y is the number of sets of furniture to be produced.