An art professor wishes to take his class on a trip to the Art Institute of Chicago. The Art Institute has several different pricing options for groups:
$\cdot$ $25 per person for group sizes up to 14 people (this is the standard individual rate); $\cdot$$ 22 per person for group sizes from 15 to 25 people;
$\cdot$ $18 per person for group sizes of 26 people or more. For groups of at least 15 people, the group must also book their tickets ahead of time, and pay a flat reservation fee of$ 10. For groups of size 14 people or fewer, there is no reservation fee.

a) Fill in the missing values of the table showing the cost of admittance, $C(n)$ for a group of $n$ people, for $n$ from 0 to 30, in increments of 5 people.

 $n$ 0 5 10 15 20 25 30 $C(n)$

b) Write a piecewise function for $C(n)$.

for
$0\leq$$x\leq$
$C(n)=$
for
$\leq x\leq$
for
$\leq x$

c) How much will it cost to buy tickets for the professor plus 18 students?
dollars

d) If the professor's budget is \$ 325, how many students can he take (that is, how many people in addition to himself)?
students