1. Define operations research. Explain the six major phases of operations research. (08 Marks) (Dec.2019/Jan.2020)

2. Solve the Linear programming problem graphically. (08 Marks) (Dec.2019/Jan.2020)

Zmax = 20X₁ + 24X₂

Subject to: 2X₁ + 3X₂ <= 1500

3X₁ + 2X₂ <= 1500

X₂ <= 450 and

X₁, X₂ >= 0

3. Old hens can be bought at Rs.50 each but young ones cost Rs.100 each. The old hens lay 3 eggs/week and young hens 5 eggs/week. Each egg costs Rs.2. A hen costs Rs. 5 per week to feed. If a person has only Rs. 2000 to spend for hens, formulate the problem to decide how many of each kind of hen should, he buy? Assume that he cannot house more than 40 hens. (08 Marks) (Dec.2019/Jan.2020)

4. With reference to Linear Programming Problem (LLP) define the following: i) Feasible solution ii) Unbounded solution iii).Optimal solution iv) Feasible region. (08 Marks) (Dec.2019/Jan.2020)

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5. Define operation research. List and explain the various phases of an operation research study. (08 Marks) (June/July 2019)

6. A firm manufactures three products A, B and C. The profits per unit product are Rs.3, Rs.2 and Rs.4 respectively. The firm has two machines and the required processing time in minutes for each machine on each product is given below:

	Product
Machine	A	B	C
X	4	3	5
Y	2	2	4

Machines X and Y have 2000 and 1500 machine-minutes respectively. The firm must manufacture 100 A's, 200 B's and 50 C's but not more than 150 A's. Set up an LP model to maximize the profit. (08 Marks) (June/July 2019)

7. Use the graphical method to solve the following LPP: (12 Marks) (June/July 2019)

Maximize Z = x + 0.5y

Subject to constraints 3x + 2y <= 12

5x <= 10

X + y <= 18

-x + y >= 4

Where x, y >= 0

8. Define: i) Feasible solution ii) unbounded solution iii) Feasible region iv) Optimal solution. (04 Marks) (June/July 2019)

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9. Define operations research. Explain the phases of operations research. (07 Marks) (Dec.2018/Jan.2019)

10. A firm manufactures two types of products A and B and sells them at a profit of Rs.2 on type A and Rs.3 on type B. Each product is processed on two machines G and H. Type A requires one minute of processing time on G and two minutes of on H. Type B requires one minute of processing time on G and one 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. How many items of Type A and Type B should be produced so that the total profit is maximum? Formulate this problem as LPP. (05 Marks) (Dec.2018/Jan.2019)

11. Using Graphical method solve the following: (04 Marks) (Dec.2018/Jan.2019)

Maximize Z = 5x₁ + 4x₂

Subject to 6x₁ + 4x₂ <= 24

X₁ + 2x₂ <= 1

X₂ <= 2 and

X₁, x₂ >= 0.

12. Old hens can be bought at Rs.2 each and young ones at Rs. 5 each. The old hens lay 3 eggs per week and the young ones lay 5 eggs per week, each egg being worth 30 paisa. A hen (young or old) costsRs.1 per week to feed. You have only Rs. 80 to spend for buying hens. How many of each kind should you buy to give a profit of more than Rs.6 per week assuming that you cannot house more than 20 hens? Formulate the problem as an LPP. (06 Marks) (Dec.2018/Jan.2019)

13. Using graphical method solve the LPP: (06 Marks) (Dec.2018/Jan.2019)

Minimize Z = 20x₁ + 10x₂

Subject to x₁ + 2x₂ <= 40

3x₁ + x₂ >= 30

4x₁ + 3x₂ <= 60 and

x₁, x₂ >= 0.

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14. Write the meaning of following terms with respect to a LPP: i) Feasible solution ii) Infeasible solution iii) Optimal solution iv) Unsounded solution. (04 Marks) (Dec.2018/Jan.2019)

15. Define operations research. List and explain the various phases of an operations research study. (06 Marks) (June/July 2018)

16. An agriculturist has a farm with 126 acres. He produces Tomato, Mango and Potato. Whatever he raises is fully sold in the market. He gets Rs.5/- for Tomato/kg, Rs.4/- for Mango/kg and Rs.5/- for Potato/kg. The average yield is 1,500 kg of Tomato/acre. 1800 kg of Mango/acre and 1200kg of Potato/acre. To produce each 100kg of Tomato and Mango and to produce each 80kg of Potato a sum of Rs.12.50 has to be used for manure. Labour required for each acre to raise the crop is 6 man-days for Tomato and Potato each and 5 man-days for Mango. A total of 500 man-days of labour at a rate of Rs.40/- per man day are available. Formulate this as a LP model to maximize the agriculturist's total profit. (10 Marks) (June/July 2018)

17. Define: i) Feasible region ii) Feasible solution iii) Optimal solution (06 Marks) (June/July 2018)

18. Solve the following LPP by graphical method. (10 Marks) (June/July 2018)

Minimize Z = 20x₁ + 10x₂

Subject to x₁ + 2x₂ <= 40

3x₁ + x₂ >= 30

4x₁ + 3x₂ >= 60

x₁, x₂ >= 0

19. Define OR. Explain the nature and impact of OR. (10 Marks) (Dec.2017/Jan.2018| 10 Scheme)

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20. Old hens can be bought at Rs. 2 each but young ones at Rs. 5 each. The old hens lay 3 eggs per week and the young ones lay 5 eggs per week, each egg being worth 30 paisa. A hen (young/old) costs Rs. 1 per week to feed. You have only Rs. 80 to spend for buying hens. How many of each kind should you buy to give a profit of more than Rs. 6 per week, assuming that you cannot house more than 20 hens. Write a mathematical model of the problem. (10 Marks) (Dec.2017/Jan.2018| 10 Scheme)

21. Explain the concept of tie breaking in simplex method. (10 Marks) (Dec.2017/Jan.2018| 10 Scheme)

22. Use simplex method to solve the following LPP: (10 Marks) (Dec.2017/Jan.2018| 10 Scheme)

Maximize Z = 4x₁ + 10x₂

Subject to constraints: 2x₁ + x₂ < 50

2x₁ + 5x₂ = 100

2x₁ + 3x₂ < 90 and

x₁, x₂ > 0.

23. What are different phases of operation research? Briefly explain phases of operations research study. (08 Marks) (Dec.2016/Jan.2017 | 10 Scheme)

24. Old hens can be brought at Rs 50/each but young ones cost 7100/- each. The old hens lay 3 eggs/week and young ones lay 5 eggs/week. Each egg sold at Rs 2/-. A hen costs Rs 5/week to feed. If a person has only Rs 3000/- to spend for hens. Formulate the problem to decide how many of each kind of hen should he buy? Assume that he cannot house more than 30) hens, (06 Marks) (Dec.2016/Jan.2017 | 10 Scheme)

25. Define the following with respect to a LPP. Give example for each: (i) Feasible solution (ii) Feasible region (i) Infeasible solution (06 Marks) (Dec.2016/Jan.2017 | 10 Scheme)

26. Solve the following LPP by using graphical method: (8 Marks) (Dec.2016/Jan.2017 | 10 Scheme)

Maximize Z = 5x1 + 4x2

Subject to 6x1 + 4x2 <= 24

X1 + 2x2 <= 6

X1 + x2 <= 1

X2 <= 2

Where x1, x2 >= 0

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27. Define operations research. Explain the phases of operations research. (08 Marks) (June/July 2017 | 10 Scheme)

28. A firm can be produced 3 types of body sweaters say A, B and C. Three kinds of wool are required for it, say red wool, green wool and blue wool. One unit of type A sweater needs 2 yards of red wool and 3 yards of blue wool, one unit of type B sweater needs 3 yards red wool 2 yards of green wool and 2 yards of blue wool. One unit of type C sweater needs 5 yards of green wool and 4 yards of blue wool. The firm has only a stock of 80 yards of red wool, 100 yards of green wool and 150 yards of blue wool. It is assumed that the income obtained from each unit of type A sweater is Rs. 30, type B sweater is Rs. 50 and type C sweater is Rs. 40. Formulate this problem as LPP. (05 Marks) (June/July 2017 | 10 Scheme)

29. Using graphical method solve the following: (07 Marks) (June/July 2017 | 10 Scheme)

Maximize Z = 3000x₁ + 2000x₂

Subject to x₁ + 2x₂ <= 6

2x₁ + x₂ <= 8

X₂ <= 2

X₁ + x₂ <=1

And x₁, x₂ >= 0