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 is to 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.