Maximizing profit: Suppose you own a tour bus and you book groups of 20 to 70 people for a day tour. The cost per person is $30 minus $0.25 for every ticket sold. If gas and other misc costs are $200, how many tickects should you sell to maximize your profit? Treat the number of tickets as a nonnegative real number.

Question

Mathematics

Cohen Henry

14 January, 18:17

Maximizing profit: Suppose you own a tour bus and you book groups of 20 to 70 people for a day tour. The cost per person is $30 minus $0.25 for every ticket sold. If gas and other misc costs are $200, how many tickects should you sell to maximize your profit? Treat the number of tickets as a nonnegative real number.

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Dulce · Answer 1

Revenue:

R (x) / x = 30 - 0.25 x

R (x) = 30 x - 0.25 x²

Profit:

P (x) = 30 x - 0.25 x² - 200

P ' (x) = 30 - 0.5 x

30 - 0.5 x = 0

0.5 x = 30

x = 60

P max = 30 · 60 - 0.25 · 3600 - 200 = $700

Answer:

I should sell 60 tickets to maximize the profit.