Question

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.

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.