Question 127434
During the next production cycle, 1,200 hours of labor are available under a union agreement. 
The firm also has a stock of 3,500 feet of good quality redwood.
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Let # of benches produced be "b"; Let # of picnic tables produced be "P". 
Each bench that Outdoor Furniture produces requires 4 labor hours and 10 feet of redwood: 
each picnic table takes 6 labor hours and 35 feet of redwood. 
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Labor Inequality: 4b+6p <= 1200
Redwood Inequality: 10b+35p <= 3500

Completed benches will yield a profit of $9 each, and tables will result in a profit of $20 each.
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Objective Function: Profit = 9b+20p
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How many benches and tables should Outdoors Furniture produce to obtain the largest possible profit? Use graphical Linear programming approach.
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INEQUALITIES:
Labor: p <= (-2/3)b + 200
Redwood: p <= (-2/7)b + 100
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Graph the solution sets of both inequalities:
{{{graph(400,300,-10,320,-10,220,(-2/3)x+200,(-2/7)x+100)}}}
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Determine the vertices of the solution set:
(0,100), (262.5,25) (300,0)
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Check each vertex pair in the objective function to see which pair
yields the maximum profit.
Profit = 9b+20p
(0,100) yields: 2000
(262.5,25) yields: 9*262.5+20*25=2862.50
(300,0) yields 9*300 = 2700
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Conclusion: maximum comes with 263 benches and 25 picnic tables.
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Cheers,
Stan H.