In a chemical industry, two products A and B are made involving two operations. The production of B also results in a by-product C. The product A can be sold at Rs. 3 profit per unit and B at Rs. 8 profit per unit. The by-product C has a profit of Rs. 2 per unit, but it cannot be sold as the destruction cost is Re. I per unit. Forecasts show that up to 5 units of C can be sold. The company gets 3 units of C for each unit of A and B produced. Forecasts show that they can sell all the units of A and B produced. The manufacturing times are 3 hours per unit for A on operation one and two respectively and 4 hours and 5 hours per unit for B on operation one and two respectively. Because the product C results from producing B, no time is used in producing C. The available times are 18 and 21 hours of operation one and two respectively. The company question: how much A and B should be produced keeping C in mind to make the highest profit. Formulate LP model for this problem..
