SOLUTION: 20) John owns a hotdog stand. He has found that his profit is represented by the equation P(x) = -x2 + 66x + 82, with P being profits and x the number of hotdogs sold. How many h

Algebra ->  Linear-equations -> SOLUTION: 20) John owns a hotdog stand. He has found that his profit is represented by the equation P(x) = -x2 + 66x + 82, with P being profits and x the number of hotdogs sold. How many h      Log On


   

Question 126795: 20) John owns a hotdog stand. He has found that his profit is represented by the equation
P(x) = -x2 + 66x + 82, with P being profits and x the number of hotdogs sold. How many
hotdogs must he sell to earn the most profit?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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 = %28-b%29%2F%282a%29
In this equation: a = -1; b = 66, so we have:
x = %28-66%29%2F%282%2A-1%29 = %28-66%29%2F%28-2%29 = +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!!