1. Note down the applications of operations research.
2. Write down meanings of operations research.

3. A person requires at least 10 and 12 units of chemicals A and B respectively, for his garden. A liquid product contains 5 and 2 units of A and B respectively per bottle. A dry product contains 1 and 4 units of A and B respectively per box. If the liquid product sales for Rs. 30 per bottle, dry product sales for Rs. 40 per box. How many of each should be purchased in order to minimize the cost and meet the requirements? Formulate the L.P.P.

4. A firm manufactures two types of products A and B and sells them at a profit of Rs. 200 on type A and Rs. 300 on type B. each product is processed on two machines G and H. type A requires 1 minute of processing time on G and 2minutes on H; Type B requires 1 minute on G and 1 minute on H. the machine G is available for not more than 6 hours, 40 minutes while H is available for 10 hours during any working day. Formulate this problem as a linear programming problem.

5. A firm manufactures headache pills in two sizes A and B. size A contains 2 grains of aspirin , 5 grains of bicarbonate and 1 grain of codeine. Size B contains 1 grain of aspirin, 8 grains of bicarbonate and 6 grains of codeine. It is found by users that it requires at least 12 grains of aspirin, 74 grains of bicarbonate and 24 grains of codeine for providing immediate effect. It is required to determine the least number of pills a patient should take to get immediate relief. Formulate the problem as a LPP.

1) | D D D D Supply 6 4 1 5 02 89 2 17 16 0 4 3 6 12 5 Dem.6 10 15 4 Obtain the initial solution to above TP using northwest corner method. D1 D2 D3 D4 Supply 01 1 2 3 4 6 O2 4 3 2 0 8 03 0 2 2 1 10 Demand 4 6 8 6 Obtain the initial solution to above TP using least cost method. 3.) Solve this transportation problem A B C D Supply 6 3 5 4 22 15 9 2 7 15 HII 5 7 8 6 8 Demand 7 12 1791 4.Find the assignment of salesmen to various districts which will result minimum cost. Salesman District 1 2 3 4 16 10 14 11 14 11 15 15 15 15 13 12 | 13 12 14 15