Question

Last year, tickets to a play were sold for $11 each and 400 people attended. An analysis has shown that for every $1 increase in ticket price attendance will decrease by 20 people. Determine the maximum possible revenue. What ticket price with produce the maximum revenue. Show work.

Answer 1

do you have an function made up for the story problem?

Answer 2

Do I have one? Nope.

Answer 3

"Last year, tickets to a play were sold for $11 each and 400 people attended."
so the function for this would look like:
revenue = (cost)*(people)

"An analysis has shown that for every $1 increase in ticket price attendance will decrease by 20 people."
so the function for this will be the same
revenue = (cost)*(people) but we have to introduce in the increase in ticket price and the decrease people.
so,
how would we write the "cost" part to illustrate a varying increase from 11 dollars?

Answer 4

revenue= (cost+1)*(people-20) ?

Answer 5

yep,
now i'm gonna refine it and you'll get it when I do.
revenue= (cost+1)*(people-20)
revenue= (11+1)*(400-20)
revenue= (11+x)*(400-20x)

Answer 6

now it is in terms of x, where x is varying and can be incrimented to show the increase in cost and the decrease of attendence

Answer 7

so to find the max, derivate the equation we made, set it equal to zero, and solve for x. then take x+11 and that equals the ticket price to maximize revenue

Answer 8

Thank you so much!

Answer 9

yep!