Question

Charter Revenue The owner of a luxury motor yacht that sails among the 4,000 Greek Islands charges $560 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 $6 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 giving the revenue per day (in dollars) realized from the charter REX) (b) What is the revenue per day (in dollars) ir 4 people sign up for the cruse? $ (c) What is the revenue per day (in dollars) if 61 people sign up for the cruise

Answer 1

a) It is given that at least 20 people sign up for the cruise. For each additional person, the fare is reduced by $6 for all. If there are x additional passengers, then the total number of people is (20+x) and fare becomes $(560-6x)

Therefore,

R(x) = (560 6.0) (20+2)

b) If there are 54 people who sign up for the cruise. Then,

= 54 – 20 = 34

and revenue generated is

$(560 – 6 x 34) x 54 = $356 x 54 = $19,224

c) If there are 61 people who sign up for the cruise. Then,

r = 61 - 20 = 41

and revenue generated is

$(560 – 6 x 41) x 61 = $314 x 61 = $19,154