The owner of a luxury motor yacht that sails among the 4000 Greek islands charges $600/person/day if exactly 20 people sign up for the cruise. However, if more than 20 people sign up (up to the maximum capacity of 90) for the cruise, then every fare is reduced by $4 for each additional passenger. Assuming that at least 20 people sign up for the cruise, determine how many passengers will result in the maximum revenue for the owner of the yacht. What is the maximum revenue

85 Passengers (20 plus additional 65) will result in maximum revenue for the owner of the yacht. Maximum Revenue will be $28,900.

Explanation:

current: 20 passengers at $600 each

let the number of additional passengers be x

cost per passenger = 600 - 4x

revenue (R) = (20+x)(600-4x)

= 12000 - 80x + 600x -4 x^2

dR/dx = -80 + 600 - 8x = 0 for a max of R

8x = 520

x = 65

There should be an additional 65 or a total of 85 passengers

The cost per passenger would be 600-4(65) or $340 per day

Maximum revenue for the yacht:

revenue (R) = (20+x)(600-4x)

revenue (R) = (20+65)(600-4(65))

revenue (R) = (85)(600-260)

revenue (R) = $28,900

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