Two products, A and B, are made that each involve two chemical operations. Each unit of product A requires 2 hr on operation 1 and 4 hr on operation 2. Each unit of product B requires 3 hr on operation 1 and 4 hr on operation 2. Available time for operation 1 is 16 hr, and for operation 2 it is 24 hr. The production of product B also results in a by-product C at no extra cost. Although some of this by-product can be sold at a profit, the remainder has to be destroyed. Product A sells for $4 profit per unit, while product B sells for $10 profit per unit. Byproduct C can be sold at a unit profit of $3, but if it cannot be sold, the destruction cost is $2 per unit. Forecasts show that up to five units of C can be sold. The company gets two units of C for each unit of B produced.
Determine the production quantity of A and B, keeping C in mind, so as to make the largest profit.