SOLUTION: not sure how to set up and do an airport shuttle has an average of 1200 passengers per day and charges 15 per ride. Each 1 dollar increase in fare results in a loss of 50 riders.

Question 201313: not sure how to set up and do
an airport shuttle has an average of 1200 passengers per day and charges 15 per ride. Each 1 dollar increase in fare results in a loss of 50 riders. What should the fare be to maximize the revenue?
can someone help please
thanks

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
an airport shuttle has an average of 1200 passengers per day and charges 15 per ride. Each 1 dollar increase in fare results in a loss of 50 riders. What should the fare be to maximize the revenue?
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Revenue = (# of passengers)(charge per passenger)
Let the dollar increase be x dollars.
Equation:
R(x) = (1200-50x)(15+x)
R(x) = 50(24-x)(15+x)
R(x) = 50(360 + 9x - x^2)
Maximum R occurs when x = -b/2a = -9/-2 = 4.5
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Maximum Revenue occurs when the price is 15 + 4.5 = $19.50
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Cheers,
Stan H.
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