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.

A firm manufactures two types of products, A and B, and sells them at a profil of 3 per unit to type B product and 5 perunit of type A product. Both product is processed on two machines M1and M2 One unit of type A requires one minute of processing time on M1 and two minutes of processing time on M2i whereas one unit of type B requires one minute of processing time on M1 and one minute on M Machines sells them at a profit of 5 per unit of type A and M, and M, are respectively available for at most 5 hours and 6 hours in a day. Find out how many units of each type of product the firn should produce a day in order to maximize the profit. Solve the problem graphically [CHSE 2000]

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.

A manufacturer produces two products A and B. Both the products are processed on two different machines. The available capacity of first machine is 12 hours and that of second machine is 9 hours per day. Each unit of product A requires 3 hours on both machines and each unit of product B requires 2 hours on first machine and 1 hour on second machine. Each unit of product A is sold at Rs. 7 profit and that of B at a profit of Rs. 4. Find the production level per day for maximum profit graphically.

A company manufactures two types of screws A and B. all the screws have to pass through a threading machine and a slotting machine. A box of type A screw requires 2min on the threading machine and 3 min on the slotting machine. A box of type B screw requires 8 min on the threading machine and 2 min on the slotting machine. In a week each machine is availbale for 60h. On selling these screws, the company gets a profit of 100 box on type A screw and 170 per box on type B screws. Formulate this problem as a LPP given that the objective is to maximise profit.

A firm manufactures 3 products A, B and C. the profits are Rs. 3, 2 and 4 respectively. The firm has 2 machines and below is the required processing time in minutes for each machine on each product. Machine Products A B C M_1 M_2 4 2 3 2 5 4 Machines M_1a n d\ M_2 have 2000 and 25000 machine minutes respectively. The firm must manufacture 100 As, 200B and 50Cs but not more 150 As. Set up a LPP to maximize the profit.

A company is making two products A and B. The cost of producing one unit of products A and B are Rs. 60 and 80 respectively. As per the agreement, the company has to supply at least 200 units of product B to its regular customers. One unit of product A requires one machine hour whereas product B has machine hours available abundantly within the company. Total machine hours available for product A are 400 hours. One unit of each product A and B requires one labour hour each and total of 500 labour hours are available. The company wants to minimize the cost of production by satisfying the given requirements. Formulate this problem as a LPP.

A company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type A require 5 minutes each for cutting and 10 minutes each for assembling. Souvenirs of type B require 8 minutes each for cutting and 8 minutes each for assembling. There are 3 hours 20 minutes available for cutting and 4 hours for assembling. The profit is Rs 5 each for type A and Rs 6 each for type B souvenirs. How many souvenirs of each type should the company manufacture m order to maximise the profit?

A manufacturer manufactures two types of tea-cups, A and B. Three machines are needed for manufacturing the tea cups. The time in minutes required for manufacturing each cup on the machines is given below: Each machine is available for a maximum of six hours per day. If the profit on each cup of type A is Rs 1.50and that'on each cup of type B is Rs 1.00, find the number of cups of each type that should be manufactured in a day to get maximumprofit.

Two bodies of masses m_1 and m_2(

A manufacturer makes two types of toys A and B. Three machines are needed for this purpose and the tune (in minutes) required for each toy on the machines is given below: Each machine is available for a maximum of 6 hours per day. If the profit