The owner of a luxury motor yacht that sails among the 4000 Greek islands charges $630 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 $4 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.

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

What is the revenue per day if 41 people sign up for the cruise?

What is the revenue per day if 88 people sign up for the cruise?

see the first related question below

To find a function R that gives the revenue per day realized from the charter, we need to consider the different scenarios based on the number of passengers.

First, let's determine the number of additional passengers above 20, denoted by x. Note that we assume at least 20 people sign up for the cruise, so x can take values from 0 to 70.

When there are exactly 20 people on board, each person pays $630 per day. Therefore, the revenue per day is:
R(20) = $630 * 20

When there are more than 20 people (20 + x) on board, each fare is reduced by $4 per day for each additional passenger. So, the fare per person is:
Fare = $630 - ($4 * x)

The total revenue per day is then given by:
R(x) = Fare * (20 + x)

To find the revenue per day when 41 people sign up for the cruise, we substitute x = 41 - 20 = 21 into the function R(x):
R(21) = ($630 - ($4 * 21)) * (20 + 21)

To find the revenue per day when 88 people sign up for the cruise, we substitute x = 88 - 20 = 68 into the function R(x):
R(68) = ($630 - ($4 * 68)) * (20 + 68)

Now, we can calculate the revenue per day for both cases using the above formulas.