Question 126795
P(x) = -x^2 + 66x + 82, with P being profits and x the number of hotdogs sold. 
How many hotdogs must he sell to earn the most profit?
:
The max of this equation occurs at the axis of symmetry, we can find that be
using the formula x = {{{(-b)/(2a)}}}
In this equation: a = -1; b = 66, so we have:
x = {{{(-66)/(2*-1)}}} = {{{(-66)/(-2)}}} = +33
:
We can say his max profit occurs when he sell 33 hot dogs
:
You can find out what amt that profit is, by substituting 33 for x in the original equation and finding P(x)
:
From a practical point of view, this does not make sense in the real world.
 Using this equation, he would make over $1171 when he sold 33 hot-dogs!!