A small firm makes three products, which all follow the same three step process, which consists of milling, inspection, and drilling. Product A requires 6 minutes of milling, 5 minutes of inspection, and 4 minutes of drilling; product B requires 2.5 minutes of milling, 2 minutes of inspection, and 2 minutes of drilling; and product C requires 5 minutes of milling, 4 minutes of inspection, and 8 minutes of drilling. The department has 20 hours available during the next period for milling, 15 hours for inspections, and 24 hours for drilling. Product A contributes $6 per unit to profit, product B contributes $4 per unit, and product C contributes $10 per unit.
At the optimum solution, what is the company's profit during the next period?
How many units of each are produced at the optimal solution (use numbers)?