Problem $19-4($Algo$)$

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 $\frac{2}{3}$ pound raisins and $\frac{1}{3}$ pound peanuts,

and the standard mix has $\frac{1}{2}$ pound raisins and $\frac{1}{2}$ 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

$$3\mathrm{.}60$ for a one$-$pound bag, and the standard mix will sell for

$$3\mathrm{.}15$ for a one$-$pound bag. The owner estimates that no more

than $170$ bags of one type can be sold.

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

should be prepared?

$.$ What is the expected profit?