the function f(t)=-0.00405x^2 +8.15x-100, what is the maximum amount of profit he will make? How many hot dogs does he have to sell in order for him to earn thi

Question

Hot Diggity Dogs is a concession choice at pensacola Blue Wahoos Stadium. The owner of the stand has figured that he can project the amount of the profit he will make per game based on the number of hot dogs he sells. If his profit is modeled by the function f(t)=-0.00405x^2 +8.15x-100, what is the maximum amount of profit he will make? How many hot dogs does he have to sell in order for him to earn this much profit? He will lose money on his concession stand until he sells how many hotdogs? 

Answer 1

Set the derivative of f(t) equal to zero.

 

f'(t) = 0

 

-0.0081t + 8.15 = 0

 

 

Solve for t.  This only value of t is your critical value.  It also represents the amount of hotdogs he must sell to get his maximum profit.

 

Evaluate f(t) at this critical value to get the maximum amount.

 

 

He will loose money  when f(t)=0.   Solve for t to find the amount of hotdogs of loss profit.

Answer 2

For f(x) = ax² + bx + c the maximum, or minimum, occurs at -b/2a.

In this case -8.15 / 2(-0.00405)

Can you calculate?