Q$\mathrm{.}1.(30$ pnts$.)$ Suppose you have a rod of length $n,$ and you want to cut up the rod and sell the pieces in a way that maximizes the total amount of money you get. A piece of length $i$ is worth $p_i$ dollars.

Let Length i and Price $p_i$ be as follows:

$\backslash$table$[[$Length $i,1,2,3,4,5,6,7,8,9,10$