PLEASE I NEED IT FAST AND EXPLAINED IN DETAIL!!!!!

Question

A food truck sells 100 hot dogs each day when it charges $2.00 per hot dog. For a $0.25 decrease in price, the food truck sells 25 more hot dogs.

a.  How much should the food truck charge to maximize daily revenue?

The food truck should charge $ per hot dog.

b. What is the maximum daily revenue?

The maximum daily revenue is $. 

Answer 1

To solve this, let's first set up the equation for daily revenue of the hot dog stand.

R = (100 + x) * (2.00 - x/100)

R = total revenue

x = number of hot dogs sold over 100

R = -x²/100 + x + 200

Take the derivative of this function, set it equal to zero, and solve for x.

0 = -x/50 + 1

x/50 = 1

x = 50

The food truck should sell 150 hot dogs to maximize its revenue. That means hot dogs will be sold for $1.50 each for a total revenue of $225.