During the summer months Terry makes and sells necklaces on the beach. Terry notices that if he lowers the price, he can sell more necklaces, and if he raises the price than he sells fewer necklaces. The table below shows how the number $n$ of necklaces sold in one day depends on the price $p$ (in dollars). $$\begin{array}{|r|r|} \hline \mbox{Price} & \mbox{Number of necklaces sold} \cr \hline 7 & 34 \cr \hline 12 & 25 \cr \hline 15 & 13 \cr \hline \end{array}$$
(a) Find a linear function of the form $n = c_0 + c_1 p$ that best fits these data, using least squares.
$n = n(p) =$

(b) Find the revenue (number of items sold times the price of each item) as a function of price $p$.
$R = R(p) =$ .

(c) If the material for each necklace costs Terry $4$ dollars, find the profit (revenue minus cost of the material) as a function of price $p$.
$P = P(p) =$ .

(d) Finally, find the price that will maximize the profit.
$p=$ .