As a company, setting the price of their product too low or too high can mean sub$-$optimal profits.

You decide to set up a hamburger stand at the Chesapeake Arena and project that your profits will

be P$($x$)=1/2$ x$^2+6$x $+402,$ where P$($x$)$ is your profit and x is the price of a hamburger. Find the

maximum profit your stand could make and the price you should sell your hamburgers at$.$