Last year, 350 people come to see a spring concert at REL. The cost per ticket was $5.00. The orchestra committee wants to increase ticket prices but it is estimated that for each increase in $0.25, 10 fewer people will attend the concert. What should the committee set the ticket price to maximize ticket sales.

Question

Mathematics

Guest

14 February, 08:50

Last year, 350 people come to see a spring concert at REL. The cost per ticket was $5.00. The orchestra committee wants to increase ticket prices but it is estimated that for each increase in $0.25, 10 fewer people will attend the concert. What should the committee set the ticket price to maximize ticket sales.

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Answers (2)

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Jaelyn Rich · Answer 1

Let 0.25x is the price increase. Therefore, the number of attendees will be 350-10x and the revenue R = (350-10x) * (5+0.25x) = 1750+37.5x-2.5x^2. This parabola has maximum at x=10, meaning the price=7.5

Melanie · Answer 2

max: 10 price: 7.5