A chemical engineering company manufactures two products, A and B. Both these products involve two chemical operations for each.

A chemical engineering company manufactures two products, A and B. Both these products involve 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, 24 hours. The production of B also results in a by‑product C at no extra cost. A part of this by‑ product can be sold at a profit, but the remainder has to be destroyed.

           Product A sells for P1 rupees profit per unit while product B sells for P2 rupees profit per unit. By product C can be sold at a unit profit of P3 rupees, but if it cannot be sold it must be destroyed; the destruction cost is P4 rupees per unit. Forecasts by sales department show that a maximum of K units of C can be sold; n units of C result for every unit of B produced.

           Formulate a linear programme to determine the production quantities of A and B, keeping C in mind, so that the total profits will be maximized.