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 $670 per person per day if exactly 20 people sign up for the cruise. However, if more than 20 people (up to the maximum capacity of 90) sign up for the cruise, then each fare is reduced by $7 per day for each additional passenger. Assume at least 20 people sign up for the cruise, and let x denote the number of passengers above 20. (a) Find a function R giving the revenue per day realized from the charter.

R(x) = ???

(b) What is the revenue per day if 42 people sign up for the cruise?
$ = ?

(c) What is the revenue per day if 86 people sign up for the cruise?
$ = ?

Explanation / Answer

Suppose x is variable ;

x = No.of passengers - 20 ;

1) R(x) = (20+x)(670-7x) = 13400 + 530 x - 7x^2 ;

b) for this x = 42 - 20 = 22

so R = $21672

c) for this x = 86 - 20 = 66

so R = $17888

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