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. Determine the optimal mix of products in terms of maximizing contribution to profits for the period. Requirements: a) Define the decision variables; b) Show the business objective and objective function; c) List all constraint equations; d) Create an EXCEL working sheet for the linear programming model; e) Provide both Answer and Sentivity reports; f) Find the range of optimality for the profit coefficient of each variable using the reoprts generated.