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Question 110452: 1. Matrix methods can be used to solve linear programming problems. A linear programming problem is used to find an optimal solution, subject to stated restraints.
One typical application is to maximize profits. For example, a beauty parlor provides both highlighting and permanent wave services. It costs $5 in materials and requires 30 minutes to provide highlighting. However, it costs $12 in materials but requires 80 minutes to provide a perm. The store has at most $120 in materials and 800 minutes in labor per day to expend.
How many highlighting services and how many perms can the beauty parlor perform daily to maximize cost and time?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! One typical application is to maximize profits. For example, a beauty parlor provides both highlighting and permanent wave services.
It costs $5 in materials and requires 30 minutes to provide highlighting.
It costs $12 in materials but requires 80 minutes to provide a perm.
The store has at most $120 in materials and 800 minutes in labor per day to expend.
How many highlighting services and how many perms can the beauty parlor perform daily to maximize cost and time?
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Let "h" be # of highlighting jobs ; Let "P" be # of perm jobs.
h>=0
p>=0
Materials Inequality : 5h + 12m <= 120
Time Inequality : 30h + 80m <= 800
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Graph these equations on a h/m coordinate system.
h <= (-12/5)m+24
h <= (-8/3)m + 80/3
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Find the vertices of the solution space:
(0,0), (0,24), (0,10)
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Determine Profit at these vertex values:
(0,0) implies 0 profit
(0,24) implies 12*24 = $288 profit
(0,10 implies 12*10 = $120 profit
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Cheers,
Stan H.
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