SOLUTION: Can you please help me solve: A ferry service transporting passengers to an island charges a fare of $10 and carries 300 persons per day. The manager estimates that the company wil
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Question 74196This question is from textbook Algebra and Trigonometry Structure and Method
: Can you please help me solve: A ferry service transporting passengers to an island charges a fare of $10 and carries 300 persons per day. The manager estimates that the company will lose 15 passengers for each increase of $1 in the fare. Find the fare that yields the greatest income. This question is from textbook Algebra and Trigonometry Structure and Method
You can put this solution on YOUR website! Can you please help me solve: A ferry service transporting passengers to an island charges a fare of $10 and carries 300 persons per day. The manager estimates that the company will lose 15 passengers for each increase of $1 in the fare. Find the fare that yields the greatest income.
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Let "x" be the number of dollars the fare increases.
Then Income to the company =(10+x)(300-15x)
I(x) = -15x^2 +285x+3000
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This is a quadratic with a=-15 ; b=285 ; c=3000
Maximum income occurs when x=-b/2a = -285/-30=9.5
The fare when x=$9.50 is $19.50.
The Income will be maximum when fare is $19.50
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Cheers,
Stan H.
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