PLEASE I NEED IT FAST

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

Revenue R = PX = Price times quantity sold

P=-x/100 + 3

R = (x/100+3)X = x^2/100 + 3x

take the derivative and set equal to zero, solve for x

x/50 + 3 = 0

x = 150

P= -150/100+ 3 = $1.50

max R = 150 times $1.50 = $225

Answer 2

a quantity sold n=100+100*(2-x)=300-100x with x being the prices

total revenus f=n*x=300x-100x^2, the maximum happens at 300/200=$1.5

b the revenue is thus 300*1.5-100*1.5^2=450-225=$225