SOLUTION: A ferry service transporting passengers to an island charges a fare of $10 and carries 300 persons. The manager estimates that the company will lose 15 passengers for each increase

Question 203307: A ferry service transporting passengers to an island charges a fare of $10 and carries 300 persons. The manager estimates that the company will lose 15 passengers for each increase in fare of $1. Find the fare that yields the greatest income.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A ferry service transporting passengers to an island charges a fare of $10 and carries 300 persons. The manager estimates that the company will lose 15 passengers for each increase in fare of $1. Find the fare that yields the greatest income.
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Income = (fare)(# of passengers)
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I(x) = (10 +1x)(300-15x)
I(x) = 3000 - 150x + 300x - 15x^2
I(x) = -15x^2 + 150x + 3000
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Maximum "I" occurs when x = -b/2a = -150/(2*-15) = $5
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Fare = (10-x) = $5.00 will give maximum Income.
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Cheers,
Stan H.
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