Question 316412: 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. 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. [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. WOW these things kill me there has to be an easier way to do this than what I've been doing. I appreciate your help.
Thanks Again
Christopher
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.
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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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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.
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