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The starting price for a ticket for a high school play is $5. The auditorium capacity is 400 people. The organizer estimates that for every 10 cent increase in the ticket price 5 less people will attend the play. What is the best price and what is the maximum revenue that the school can get?

Answer :

francocanacari

The best price is $6.50, and the maximum revenue that the school can get is $2,112.50.

Price determination

Given that the starting price for a ticket for a high school play is $5, and the auditorium capacity is 400 people, and the organizer estimates that for every 10 cent increase in the ticket price 5 fewer people will attend the play, to determine what is the best price and what is the maximum revenue that the school can get, the following calculation must be made:

  • 400 x 5 = 2,000
  • 395 x 5.1 = 2,014.5
  • 390 x 5.2 = 2028
  • 350 x 6 = 2100
  • 300 x 7 = 2100
  • 325 x 6.5 = 2112.5
  • 320 x 6.6 = 2112
  • 330 x 6.4 = 2112

Therefore, the best price is $6.50, and the maximum revenue that the school can get is $2,112.50.

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