
Demand function
the problem deals with applications of derivatives. the problem is: until recently hamburgers at the city sports arena costs $4 each the food concessionaire sold an average of 10,000 hamburgers on a game night. when the price was raised to $4.40, hamburger sales dropped off to an average of 8000 per night.
a) find the price of a hamburger that will maximize the nightly hamburger revenue.
I know that in order to do that, we have to use the point slope formula to find the demand function. I got p4=[(44.4)/(10,0008000)] [(x10000).
I don't get why the answer key has p2=[(22.4)/(10,0008000)] [(x10000) and still got the correct answer?

Where did you use the derivative?
x = Price
Demand(x) = a + bx  We're assuming a linear model.
Revenue(x) = x*Demand(x) = ax + bx^2
Now we have clues:
Demand(4) = a + b(4) = 10000
Demand(4.4) = a + b(4.4)= 8000
I get a = 30000 and b = 5000
Revenue(x) = 30000*x  5000*x^2
dRevenue/dx = 30000  10000*x
Find zero: 30000  10000*x ==> x = 3
Revenue(3) = 45000
Write down definitions. Write clearly and completely. Make sure at least YOU can follow your work.

TKHunny, I don't believe that was the question. The OP was simply asking, "why did the answer key use 'p 2= =[(22.4)/(10,0008000)] [(x10000)' rather than 'p 4= [(4 4.4)/(10,000 8000)][(x 10000)' and how do both of those give the same answer?"
fabxx, all I can say is that there must have been a typo. For the given problem, yours is the correct formula and they give different answers. Using the answer key's demand function, the price that gives maximum revenue would, in fact, be $2.00.

Making up my own questions again, eh? (Doh)