

ryay New user 90 Posts 
Mike sells cars. The profit he makes each day can be modeled by the equation:
P(x)=x^2+240x700 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 141 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.

Jonathan Townsend Eternal Order Ossining, NY 27016 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

GeorgeG Inner circle Thousand Oaks, CA 1018 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?

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

TomasB Inner circle Sweden 1143 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(xa)^2 which is the same as bx^2+2xaa^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(x120)^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 4754 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

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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