The owner of a luxury motor yacht that sails among the 4000 Greek islands charges $430 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.

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

R(x) = -4x^2+350x+8600

(b) What is the revenue per day if 47 people sign up for the cruise?

$ ?

(c) What is the revenue per day if 84 people sign up for the cruise?

$ ?

To find the revenue per day for a specific number of passengers, we can use the function R(x) = -4x^2 + 350x + 8600.

(a) The function R(x) represents the revenue per day realized from the charter. In this case, x represents the number of passengers above 20.

(b) To find the revenue per day if 47 people sign up for the cruise, we need to calculate R(47).

R(47) = -4(47)^2 + 350(47) + 8600
= -4(2209) + 16450 + 8600
= -8836 + 16450 + 8600
= 9314 + 8600
= $17,914

Therefore, the revenue per day if 47 people sign up for the cruise is $17,914.

(c) Similarly, to find the revenue per day if 84 people sign up for the cruise, we need to calculate R(84).

R(84) = -4(84)^2 + 350(84) + 8600
= -4(7056) + 29400 + 8600
= -28,224 + 29400 + 8600
= -28,224 + 38,000
= $9,776

Therefore, the revenue per day if 84 people sign up for the cruise is $9,776.