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$/$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 $$4\mathrm{.}20$ for a one$-$pound bag, and the standard mix will sell for $$3\mathrm{.}75$ for a one$-$pound bag. The owner estimates that no more than $230$ 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?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$/$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 $$4\mathrm{.}20$ for a one$-$pound bag, and the standard mix will sell for $$3\mathrm{.}75$ for a one$-$pound bag. The

owner estimates that no more than $230$ 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?