A monopolist produces a single good X but sells in two separate markets. The demand function for each market is given as P$1=50-4$x$1$ and P$2=80-3$x$2.$ Total Cost$=120+8$x$,$ where x$=$ x$1+$x$2$

$($a$)$ Find the price and quantity in each market which maximize profit.

$($b$)$ What is the maximum profit