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 $2.40 per unit to profit, product B contributes $2.50 per unit, and product C contributes $3.00 per unit. Note: make sure that for every constraint the left-hand \& right-hand sides are expressed in the same unit. a. 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. (Leave no cells blank - be certain to enter " 0 " wherever required.) b. Determine the range of optimality for the three coefficients of the objective function