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Topic: For all you mathematicians 


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? 


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. 


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. 


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. 


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? 


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? 


Hi ryay, I think you want the magic Café to do your homework, right? ;)) Heinz 


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 


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 


[quote]Nir of course had the correct answer to the question actually asked. [/quote] With all due respect to Nir, I think Heinz was more on the mark :) Jack Shalom 


When it equals 0, is it when x is 237.046999107 or 2.9530008928 


When it equals 0, is it when x is 237.046999107 or 2.9530008928 