A factory produces two product `P_1a n dP_2` . Each of the product `P_1` requires 2 hrs for moulding, 3 hrs for grinding and 4 hrs for polishing, and each of the product `P_2` requires 4 hrs for moulding, 2 hrs for grinding and 2 hrs for polishing. The factory has moulding machine available for 20 hrs, grinding machine for 24 hrs polishing machine available for 13 hrs. The profit is Rs. 5 per unit of `P_1` and Rs 3 per unit of`P_2` and the factory can sell all that it produces . Formulate the problem as a linear programming problem to maximize the profit.