Question

A promoter of a show realizes that, if the price per ticket is a set at 650, only 50 people will watch the show. He also estimates that for every 50 decrease in the price of the ticket, the number of people watching the show will increase by 10. what should be the price per ticket so that the revenue (number of tickets sold x price per ticket) is a minimum? What is the maximum revenue?

Answer 1

@MARC

Answer 2

@Angle

Answer 3

@Zarkon

Answer 4

help me please i have only 30 minutes to finish this online assignment

Answer 5

-50/10 =-5 is the rate at which the the price to population is changing

so the price of a ticket is given by \(p(x)=-5(x-50)+650\)

then, for example if we have 50 people we have a price of

\(p(50)=-5(50-50)+650=650\)

and if we have 60 people then \(p(60)=-5(60-50)+650=-5\cdot 10+650=600\)

so the revenue is \(r(x)=xp(x)=x[-5(x-50)+650]\) (ie the number of tickets sold times the price per ticket)

multiply this out and find the vertex of this parabola (or use calculus)