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#### Operations Research Model Question Paper

11th Standard

Reg.No. :
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Time : 01:00:00 Hrs
Total Marks : 50
5 x 1 = 5
1. In a network while numbering the events which one of the following statement is false?

(a)

Event numbers should be unique

(b)

Event numbering should be carried out on a sequential basis from left to right

(c)

The initial event is numbered 0 or 1

(d)

The head of an arrow should always bear a number lesser than the one assigned at the tail of the arrow

2. A solution which maximizes or minimizes the given LPP is called

(a)

a solution

(b)

a feasible solution

(c)

an optimal solution

(d)

none of these

3. The minimum value of the objective function Z = x + 3y subject to the constraints 2x + y ≤20, x + 2y ≤ 20,x > 0 and y > 0 is

(a)

10

(b)

20

(c)

0

(d)

5

4. In critical path analysis, the word CPM mean

(a)

Critical path method

(b)

Crash project management

(c)

Critical project management

(d)

Critical path management

5. Given an L.P.P maximize Z=2x1+3x2 subject to the constrains x1+x2≤1, 5x1+5x2≥0 and x1≥0, x2≥0 using graphical method, we observe

(a)

No feasible solution

(b)

unique optimum solution

(c)

multiple optimum solution

(d)

none of these

6. 5 x 2 = 10
7. Construct a network diagram for the following situation:
A

8. Draw the network for the project whose activities with their relationships are given below:
Activities A,D,E can start simultaneously; B,C>A; G,F>D,C; H>E,F.

9. Draw the event oriented network for the following data:

 Events 1 2 3 4 5 6 7 Immediate Predecessors - 1 1 2,3 3 4,5 5,6
10. A toy company manufactures two types of dolls A and B. Market tests and available resources have indicated that the combined production level should not exceed 1200 dolls per week and the demand for dolls of type B is atmost half of that for dolls of type A. Further, the production level of dolls of type A can exceed three times the production of dolls of other type by at most 600 units. If the company makes profit of n2 and n6 per doll, how many of each should be produced weekly in order to maximize the profit. Formulate the above as mathematical LPP.

11. A producer has 30 and 17 units of labour and capital respectively which he can use to produce two types of goods X and Y. To produce one unit of X, 2 unit of labour and 3 units of capital are required. Similarly, 3 units of labour and 1 unit of capital is required to produce one unit of Y. If X and Yare priced at HOO and H20 per unit respectively, how should the producer use his resources to maximize the total revenue? Formulate the LPP for the above.

12. 5 x 3 = 15
13. A soft drink company has two bottling plants C1 and C2. Each plant produces three different soft drinks S1, S2 and S3. The production of the two plants in number of bottles per day are:

 Product Plant C1 C2 S1 3000 1000 S2 1000 1000 S3 2000 6000

A market survey indicates that during the month of April there will be a demand for 24000 bottles of S1, 16000 bottles of S2 and 48000 bottles of S3. The operating costs, per day, of running plants C1 and C2 are respectively Rs.600 and Rs.400. How many days should the firm run each plant in April so that the production cost is minimized while still meeting the market demand? Formulate the above as a linear programming model.

14. Maximize Z = 3x1 + 4x2 subject to x1 – x2 < –1; –x1+x2 < 0 and x1, x2 ≥ 0

15. Solve the following LPP graphically. Minimize$Z=-3{ x }_{ 1 }+4{ x }_{ 2 }$
Subject to the constraints ${ x }_{ 1 }+2{ x }_{ 2 }\le 8\quad ,{ 3x }_{ 1 }+{ 2x }_{ 2 }\le 12\quad and\quad \quad { x }_{ 1 }\ge 0,{ x }_{ 2 }\ge 2.$

16. Solve the following LPP graphically, Minimize $Z=3{ x }_{ 1 }+5{ x }_{ 2 }$
Subject to the constraints ${ x }_{ 1 }+3{ x }_{ 2 }\ge 3,\quad { x }_{ 1 }+{ x }_{ 2 }\ge 2\quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 0.$

17. Develop a network based on the following information.

 Activity A B C D B E Immediate Predecessor - - A C E F

18. 4 x 5 = 20
19. One kind of the cake requires 200 g of flour and 25 g of fat, and another kind of cake requires 100 g of flour and 50 g of fat. Find the maximum number of cakes which can be made from 5 kg of flour and 1 kg of fat assuming that there is no shortage of other ingredients used in making the cakes?

20. A manufacturer makes two types of toys A and B. Three machines are needed for this purpose and the time (min) required for each toy on the machine is given below:

 Type Machine I Machine II Machine III A 12 18 6 B 6 0 9

Each machine is available for a maximum of 6 hours/day. If the profit on each toy of type A is Rs.7.50 and for B is Rs.5. Show that 15 toys of type A and 30 of type B should be manufactured in a day to get maximum profit.

21. Every gram of wheat provides 0.1 g of proteins and 0.25 g of carbohydrates. The corresponding values of rice are 0.05 g and 0.5 g respectively. Wheat cost Rs.4 per kg and rice cost Rs.6 per kg. The minimum daily requirements of proteins and carbohydrate for an average child are 50 g and 200 g respectively. In what quantities should wheat and rice be mixed in the daily diet to provide minimum daily requirements of proteins and carbohydrate at minimum cost. Frame an LPP and solve it graphically.

22. The following table use the activities in a building project.

 Activity Duration (days) 1-2 1-3 2-3 2-4 3-4 4-5 21 26 11 13 5 11

Draw the network for the project, calculate the earliest start time, earliest finish time, latest start time and latest finish time of each activity and find the critical path. Compute the project duration.