Question 394822: Question:
Sam is an automobile manufacturer that specializes in production of an economy model and a midsize model. The price of the economy model in market is $15(,000) and the price of midsize model is $25(,000). Sam has one production plant for both. 1,200 labour hours per day are available in this plant. Production of the economy model requires 20 labour hours per car and production of the midsize requires 40 labour hours per car. Also the total daily demand for cars is 40. Sales manager of Sam wants to allocate car production to maximize daily revenue.
a) Write down your optimization problem.
b) By solving the problem graphically, what is the the solution?
Thank-you in advance.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Sam is an automobile manufacturer that specializes in production of an economy model and a midsize model.
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The price of the economy model in market is $15(,000) and the price of midsize model is $25(,000).
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Sam has one production plant for both.
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1,200 labour hours per day are available in this plant. Production of the economy model requires 20 labour hours per car and production of the midsize requires 40 labour hours per car.
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Production Inequality: 20e+40m <= 20,000
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Also the total daily demand for cars is 40.
e + m = 40
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Sales manager of Sam wants to allocate car production to maximize daily revenue.
a) Write down your optimization problem.
e >= 0
m >= 0
20e+40m <= 1200
e + m = 40
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Objective Function: Revenue = 15000e + 25000m
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b) By solving the problem graphically, what is the the solution?
Graph the equality boundaries.
e = -2m+60
e = -m + 40
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Solution:
-2m+60 = -m+40
m = 20
So e = 20
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Coordinate pairs to check: (20,20),(0,40),(30,0)
Check each of those pairs in the Objective Function
to see which gives the maximum Revenue.
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Cheers,
Stan H.
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