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.
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.
