Two products A and B are made involving two chemical operations for each. Each unit of product A requires 2 hours on Operation 1 and 3 hours on Operation 2. Each unit of product B requires 3 hours on Operation 1 and 4 hours on Operation 2. Available time for Operation 1 is 16 hours and for Operation 2 is 24 hours. The production of product B also results in a by-product C at no extra cost. Though some of this by-product can be sold at a profit, the remainder has to be destroyed. Product A sells for $8 profit per unit, while product B sells for $20 profit per unit. By product C can be sold at a unit profit of $6 per unit, but if it cannot be sold, the cost of disposal is $5 per unit. The company gets 2 units of C for each unit of B produced. Determine the optimal production quantity of A and B, keeping C in mind so as to make the largest profit.