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ryay New user 90 Posts |
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 Inner circle Munich, Germany 1390 Posts |
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 Inner circle Munich, Germany 1390 Posts |
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 Regular user North Carolina 148 Posts |
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.
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Jonathan Townsend Eternal Order Ossining, NY 27297 Posts |
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
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GeorgeG Special user Thousand Oaks, CA 977 Posts |
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?
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Heinz Weber New user Austria 83 Posts |
Hi ryay,
I think you want the magic Café to do your homework, right? ;-)) Heinz |
idris New user St. Louis, MO 38 Posts |
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
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TomasB Inner circle Sweden 1144 Posts |
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 Inner circle within a triangle 5194 Posts |
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 Jack Shalom
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drkptrs1975 Elite user North Eastern PA 452 Posts |
When it equals 0, is it when x is 237.046999107 or 2.9530008928
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drkptrs1975 Elite user North Eastern PA 452 Posts |
When it equals 0, is it when x is 237.046999107 or 2.9530008928
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