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The Magic Cafe Forum Index » » Puzzle me this... » » For all you mathematicians (0 Likes) Printer Friendly Version

ryay
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90 Posts

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Mike sells cars. The profit he makes each day can be modeled by the equation:

P(x)=-x^2+240x-700

P stands for the profit and x stands for the price of each car he sells. for what values of x will mike make a profit?
Nir Dahan
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Munich, Germany
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This sounds like a puzzle taken from junior high algebra book...
calculate the 2 roots and the solution is everything in between. (the function gets a maximum at x=120)
N.
Nir Dahan
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Munich, Germany
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This sounds like a puzzle taken from junior high algebra book...
calculate the 2 roots and the solution is everything in between. (the function gets a maximum at x=120)
N.
leonard
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North Carolina
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Why would you sell the 121st car, if you are going to lose money? Stop at 120, collect your 13,700 (dollars?), and go home.
Jonathan Townsend
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Eternal Order
Ossining, NY
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That sounds like a nice way to compute optimal price, though something is off about the demand/supply curves implied there.

IF you sell a car for more then P(120) you start losing money?
...to all the coins I've dropped here
GeorgeG
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Thousand Oaks, CA
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It's easier with simple calculus, get the first differential set to zero, P'(x)=0 so the equation becomes -2x + 240 = 0, and x=120 for a maximum or minimum; P''(x)= -2, so the curve is concave downwards for a maximum. There must be some inherent cost issue with selling more than 120 cars, though I doubt sales and profit has a bell shaped curve. Any business majors in the know?
Heinz Weber
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Austria
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Hi ryay,

I think you want the magic Café to do your homework, right?

;-))
Heinz
idris
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St. Louis, MO
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The question doesn't say number of cars but dollar value of each car sold.

Therefore he will show a profit with cars which sell for $3 to $237. (approximate) with the highest value when he sells a car for $120 with a profit of $13700. Boy, I wish I could get a job like that. <G>

Jerry
Jerry
TomasB
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Sweden
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Instead of calculating roots and differentials to find the optimum price you can rewrite the formula by "completing the square". You want to end up with something like b-(x-a)^2 which is the same as b-x^2+2xa-a^2 so you see that the constant a we look for is half of what's in front of x giving us

P(x)=13700-(x-120)^2

By just looking at that you see that the maximum value of P is 13700 and that it happens exactly when the price of a car is 120.

Nir of course had the correct answer to the question actually asked.

/Tomas
landmark
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within a triangle
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Quote:
Nir of course had the correct answer to the question actually asked.


With all due respect to Nir, I think Heinz was more on the mark Smile

Jack Shalom
drkptrs1975
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North Eastern PA
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When it equals 0, is it when x is 237.046999107 or 2.9530008928
drkptrs1975
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North Eastern PA
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When it equals 0, is it when x is 237.046999107 or 2.9530008928
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