Question 1008709: Occasionally, for extra income, I do data entry for local companies. Recently, I was doing data entry for two companies. Between the two companies, I had a total of 6 hours a week I could spend on these projects. I determined that it costs me $4 per hour for Company A projects and $1 per hour for Company B projects. I don't want to spend more than $12 in working on these projects. If my profit is $1 per hour for Company A projects and $5 per hour for Company B projects, how many hours should I spend on projects for each company to maximize my profit?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Between the two companies, I had a total of 6 hours a week I could spend on these projects. I determined that it costs me $4 per hour for Company A projects and $1 per hour for Company B projects. I don't want to spend more than $12 in working on these projects. If my profit is $1 per hour for Company A projects and $5 per hour for Company B projects, how many hours should I spend on projects for each company to maximize my profit?
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A >= 0
B >= 0
Hours:: A + B <= 6 hrs
Cost:: 4A + B <= 12 dollars
Profit:: maximize:: P = A + 5B
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Graph:: A <= -B + 6
Graph:: A <= (-B/4) + 3
Find the intersection of the two boundary lines::
B = 4 when A = 2
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Evaluate (0,6),(6,0),(4,2) in the Profit equation to mind the maximum:
(0,6) gives P = $30
(6,0) gives P = $6
(4,2) gives P = $14
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Ans: 0 hrs on A ; 6 hrs on B
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Cheers,
Stan H.
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