Question

The owner of a luxury motor yacht that sails among the 4000 Greek islands charges $540 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 48 people sign up for the cruise?
$
(c) What is the revenue per day if 78 people sign up for the cruise?
$

Answer 1

The revenue per day from the charter can be expressed using the function R(x) = (540 - 7x) * (20 + x), where x represents the number of passengers above 20. To find the revenue per day for specific numbers of passengers, substitute the values into the function.

Step-by-step explanation:

(a) To find the function R, we can start by calculating the base revenue, which is $540 per person per day when 20 people sign up for the cruise. Let x denote the number of passengers above 20. For each additional passenger, the fare is reduced by $7 per day. So, the reduction in fare per day due to additional passengers is 7x. Therefore, the function R(x) can be expressed as:

R(x) = (540 - 7x) * (20 + x)

(b) To find the revenue per day if 48 people sign up for the cruise, we can substitute x = 28 (48 - 20) into the function R(x) and calculate the value:

R(28) = (540 - 7*28) * (20 + 28)

(c) To find the revenue per day if 78 people sign up for the cruise, we can substitute x = 58 (78 - 20) into the function R(x) and calculate the value:

R(58) = (540 - 7*58) * (20 + 58)

Answer 2

Step-by-step explanation:

Charges up to 20 passengers = $540 per person per day

Total charges = 540 × 20 = $10800

If x passengers above 20 sign up for the cruise then total number of passengers = (20 + x)

Total revenue = $(20+x)

But each fare is reduced by $7 for additional passenger above 20 then revenue generated R(x) = 540(20+x) - 7x

R(x) = 10800 + 540x - 7x

R(x) = 10800 + 533x

a). Revenue per day realized R = 10800 + 533x

b). R(48) = 10800 + 48×533

= $36,384

C). R(78) = 10800 + 78×543

= $53,154