A small candy shop is preparing for the holiday season. The owner must decide how many bags of deluxe mix and how many bags of standard mix of Peanut$/$Raisin Delite to put up$.$ The deluxe mix has $2/3$ pound raisins and $1/3$ pound peanuts, and the standard mix has $1/2$ pound raisins and $1/2$ pound peanuts per bag. The shop has $90$ pounds of raisins and $60$ pounds of peanuts to work with.

Peanuts cost $$\mathrm{.}60$ per pound and raisins cost $$1\mathrm{.}50$ per pound. The deluxe mix will sell for $$2\mathrm{.}90$ for a one$-$pound bag, and the standard mix will sell for $$2\mathrm{.}55$ for a one$-$pound bag. The owner estimates that no more than $110$ bags of one type can be sold.

a$.$ If the goal is to maximize profits, how many bags of each type should be prepared?

b$.$ What is the expected profit?