The owner of a luxury motor yacht that sails among the 4000 Greek islands charge

Question

The owner of a luxury motor yacht that sails among the 4000 Greek islands charges $568/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.

A) Assuming 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?
_________ passengers

B) What is the maximum revenue?
$ __________

C) What would be the fare per passenger in this case? (Round your answer to the nearest dollar.)
____________ dollars per passenger

Explanation / Answer

Let say x people sign up

fare = 568-4x

revenue,

R(x) = x*(568-4x)

     = 568*x – 4x^2

R’(x) = 568 – 8x

put R’(x) = 0

568-8x = 0

x = 71

R’’(x) = -8

since R’’(x) is negative, x=71 maximises R(x)

A)

71 passengers

B)

R = 568*71 – 4*71^2

= $20164

C)

fare = 568-4*71

     = $ 284

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.