Peanuts cost $$0\mathrm{.}75$ per pound and raisins cost $$2$ per pound. The deluxe mix will sell for $$3\mathrm{.}5$ for a one$-$pound bag, and the standard mix will sell for $$2\mathrm{.}5$ for a one$-$pound bag. The owner estimates that $no$ more than $95$ bags $of$ one type can $be$ sold.

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

Note: Round your answers $to$ the nearest whole number.

What $is$ the expected profit?

Note: Use your UNROUNDED decision variable values from Part $a.$ Round your final answer $to$ two decimal places.A small firm makes three similar products, which all follow the same three$-$step process, consisting $of$ milling, inspection, and drilling. Product A requires $12$ minutes $of$ milling, $5$ minutes for inspection, and $10$ minutes $of$ drilling per unit; product $B$ requires $10$ minutes $of$ milling, $4$ minutes for inspection, and $8$ minutes $of$ drilling per unit; and product $C$ requires $8$ minutes $of$ milling, $4$ minutes for inspection, and $16$ minutes $of$ drilling. The department has $20$ hours available during the next period for milling, $15$ hours for inspection, and $24$ hours for drilling. Product A contributes $$2\mathrm{.}40$ per unit $to$ profit, product $B$ contributes $$2\mathrm{.}50$ per unit, and product $C$ contributes $$3\mathrm{.}00$ per unit.

Determine the optimal mix $of$ products $in$ terms $of$ maximizing contribution $to$ profits for the period.Then, find the range $of$ optimality for the profit coefficient $of$ each variable.

Note: Leave $no$ cells blank $-be$ certain $to$ enter $"0"$ wherever required.