Question 72934
A small company produces both standard (let # be x) and deluxe (let # be y) playhouses.
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The standard playhouses take 12 hours of labor to produce, and the deluxe playhouses take 20 hours. 
The labor available is limited to 800 hours per week,
Labor Inequality: 12x + 20y <=800 
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and the total production capacity is 50 items per week.
Capacity Inequality: x + y <=50
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Existing orders require the company to produce at least 10 standard playhouses and 15 deluxe playhouses per week.
x >= 10
y >= 15
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Write a system of inequalities representing this situation, where x is the number of standard playhouses and y is the number of deluxe playhouses.
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Then graph the system of inequalities. 
Solve the inequalities for y:
Labor Inequality y <= (-3/5)x+40
Capacity Inequl y <= -x+50
Note: x >= 10 tells you the Domain for the solution set.
y >=15 tells you the Range for the solution set.
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Graph the EQUALITIES: y=(-3/5)x+40; y=-x+50 to determine the boundaries of the solution set.
{{{graph(400,300,-5,70,-5,70,(-3/5)x+40,-x+50)}}}

The solution is the intersection of the inequality and equality sets 
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Cheers,
Stan H.