Question

On a sunny day,the daily profit, P dollars,of a popcorn vendor is modelled by the equation
P= -60(x-4)^2 +120
where x is the price of a bag of popcorn.

a) What should the price be to maximize daily profit ?
b) What is the maximum amount of daily profit ? On a sunny day,the daily profit, P dollars,of a popcorn vendor is modelled by the equation
P= -60(x-4)^2 +120
where x is the price of a bag of popcorn.

a) What should the price be to maximize daily profit ?
b) What is the maximum amount of daily profit ? @Mathematics

Answer 1

a) dp/dx = -120(x-4)
0 = -120x + 480
120x= 480
x = 4

b) p(4) = -60(4-4)^2 + 120 = 120

Answer 2

how did you get that ? like what are the steps ?

Answer 3

a) derivative of p .. p'(x)
and equate it to zero .. to find minimum/maximum

b) plug the value from a to get the maximum amount of daily profit ..