The owner of a luxury motor yacht that sails among the 4000 Greek islands charges $\$ 470$ 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 60 people sign up for the cruise?
(c) What is the revenue per day if 79 people sign up for the cruise?
$\endgroup$ 02 Answers
$\begingroup$I'll get you started. See if you can compute $(b), (c)$.
$(a)$ $$\begin{align}R(x) & = 20\cdot 470 + (470 - 7)x = 9400 + 463x\;\text{ dollars per day}\end{align}$$ Now $R$ to calculate the answers to $(b), (c)$
$(b)$ What is your $x$?
$(c)$ Now, what is your $x$?
Recall, for the last two questions, that $x$ denotes the number of passengers exceeding 20, so to find $x$ in each case, we need to subtract $20$ from the given number of passengers: $$x = \text{ total number of passengers } - 20$$
$\endgroup$ 1 $\begingroup$(a) R(x)= 20*470 + x(470-20*7-7x)= 9400 + x(300-7x)
For (b) and (c), you just plug your figures in (after subtracting 20)
Good luck!!
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