SOLUTION: Suppose you own a party bus and you book groups of 20 to 70 people for a day trip. The cost per person is $30 minus 25 cents for every ticket sold. If gas and other costs are $20

Question 1030225: Suppose you own a party bus and you book groups of 20 to 70 people for a day trip. The cost per person is $30 minus 25 cents for every ticket sold. If gas and other costs are $200, how many tickets should you sell to maximize your profit?
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Let x = # of tickets sold.
==> Total revenues = x(30 - 0.25x) and Total costs = 200
==> Total profits =
Taking the derivative and equating to 0 to get the extreme value,
-0.5x + 30 = 0
==> x = 30/0.5 = 60
(The 2nd derivative p" = -0.5 < 0, hence we are assured an absolute maximum.)
Therefore, he has to sell 60 tickets to maximize profits.
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