A pharmaceutical company produces two pharmaceutical products: A and B. Production of both products requires the same process, I and II. The production of B results also in a by-product C at no extra cost. The product A can be sold at a profit of Rs 3 per unit and B at a profit Rs. 8 per unit. Some of this byproduct can be sold at the unit profit of Rs. 2, the remainder has to be destroyed and the destruction cost is Rs.1 per unit. Forecast show that up to 5 units of C can be sold. The company gets 3 units of C for each unit of B produced. The manufacturing times are 3 hours per unit for A on process I and II, respectively, and 4 hours and 5 hours per unit for B on process I and II, respectively. Because the product C result from producing B, no time is used in producing C. the available times 18 and 21 hours of process I and II, respectively. Formulate this problem as an LP model to determine the quantity of A and B which should be produced, keeping C in mid, to make the highest profit to the company.
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