The owner of a luxury motor yacht that sails among the 4000 Greek islands charges $752/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 100) for the cruise, then each fare is reduced by $8 for each additional passenger. 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 What is the maximum revenue

20 passengers at $960 each

Step-by-step explanation:

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.

(a) Find a function R giving the revenue per day realized from the charter.

R(x) =

(b) What is the revenue per day if 48 people sign up for the cruise?

$

(c) What is the revenue per day if 78 people sign up for the cruise?

$

revenue (R) = (20+x)(960-8x)

= 19200 - 160x + 960x -8 x^2

dR/dx = -160 + 960 - 16x = 0 for a max of R

16x = 800

x = 50