Find the fare that yields the greatest income.

Question

A ferry service transporting passengers charges a fair 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.

Answer 1

f represents the increase in the fare

 

f(f) = (300 - 15f)(10 + f)

f(f) = 3000 +150f - 15f²

f(f) = -15t² + 150f + 3000

 

Maximum occurs at -b/2a, or -150/-30, or 5

 

A fare of 15 dollars yields the maximum income.