Problem $19-4($Static$)$

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 or 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.

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