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A factory produces two product P1a n dP2...

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.

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A firm manufactures two products A and B. Each product is processed on two machines M_1a n dM_2 . Product A requires 4 minutes of processing time on M_1 and 8 min. on M_2 ; product B requires 4 minutes on M_1 and 4 min. on M_2 . The machine M_1 is available for not more than 8 hrs 20 min. while machine M_2 is available for 10 hrs. during any working day. The products A and B are sold at a profit of Rs. 3 and Rs. 4 respectively. Formulate the problem as a linear programming problem and find how many products of each type should be produced by the firm each day in order to get maximum profit.

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