St. Joseph’s College Of Commerce (Autonomous)

End Semester Examination – APRIL 2013

1. COM – VI Semester

OPERATIONS RESEARCH

Duration: 3 Hours                                                                  Max. Marks: 100

Section – A

I Answer all questions. Each carries TWO marks.                                               (10×2=20)

1. Mention the terminologies used in formulation of a linear programming problem.
2. Explain the techniques integer programming and replacement problems.
3. Find the feasible region for the constraint 2x-y <=0
4. Why is the Big M method called so? How are artificial variables used with M and why?
5. Differentiate between an unbalanced transportation and assignment problem with the help of examples.
6. What is a trans-shipment problem?
7. How do you identify the optimum solution when applying Hungarian method.
8. Mention any two differences between PERT and CPM.
9. Describe the terms Event and Activity.
10. Mention any four limitations of OR.

Section – B

1. Answer any SIX questions. Each carries TEN marks.         (6×10=60)
2. Formulate and solve by graphical method.

A firm that assembles computers is about to start production of two new type of computers. Each type will require assembly time, inspection time and storage space. The manager of the firm would like to determine the quantity of each type of computer to be produced in order to maximize the profit generated by the sales of these computer. Profit per unit of computer type1 is Rupees 600 and computer type2 is Rupees 500. The following information has been obtained by the manager after discussing with design manufacturing and marketing personnel.

Data	Computer Type 1	Computer Type 2	Amount Available
Assembly time Per unit   Inspection time Per unit   Stroage Space	4 Hrs     2 hrs     3 cubic meters	10 Hrs     1 Hr     3 cubis meters	100 Hrs     22 Hrs.     39 cubic meters

 

12. Write any two comprehensive definitions of OR. Explain the different types of Operations Research models.
13. a) Write the dual of

Max  Z= 23x + 20y+15z

Sub to

x +2y+3z<=160

3x+10y<=230

8y-10z>=175

X<=50

Where x, y,z>=0

1. b) Solve by  Big M method

Max Z= 10x + 12y

Subject to,

X+ y = 5

X >= 2

Y<= 4

Where x, y >=0                                                                                                  (4 + 6)

 

14. The estimated sales (tons) per month in four different cities by five different managers is given below:

Managers	Cities
	A	B	C	D
P	13	15	12	14
Q	12	14	10	12
R	16	18	14	14
S	15	15	13	13
T	14	15	14	12

1. a) Find out the assignment of cities to managers in order to maximize sales.
2. b) The management wants to send one of the managers for training for improving sales performace. Who should be sent for such a training without loosing sales?

 

15. Hindusthan construction company needs 3, 3, 4 and 5 million cubic feet of fill at four earthern damsites in Punjab. It can transfer the fill from three mounds A, B and C where 2, 6 and 7 cubic million cubic feet are available respectively. Costs of transporting one million cubic feet of fill from mound to the four sites in lakhs are:

Damsites -> Mounds	I	II	III	IV
A	15	10	17	18
B	16	13	12	13
C	12	17	20	11

Find initial solution to the following transportation problem using

1. NWCM b) LCM  c) Vogel’s approximation method

Find the cost of transportation in each case. Which method gives the least cost initial solution?

16. An officer has worked on the transportation schedule from his experience.

Destination -> Source	1	2	3	Availability
A	10	7	8	45
B	15	12	9	15
C	7	8	12	40
Requirement	25	55	30

Solution given by the officer is:

Source	Destination	Units transported
A A B C C Dummy	2 3 2 1 2 3	25 20 15 25 15 10

1. Is the solution given by the officer optimum ?
2. If not find the best solution to the problem.
3. a) Draw the network diagram for the following.
4. b) Apply forward pass, backward pass and calculate earliest and latest timings of each activity
5. c) Calculate total float and identify the critical path and duration of the project.

Activity	Immediate Predcessor	Duration (weeks)
A B C D E F G	– – – A B C D,E	2 4 3 1 6 5 7

 

18. Solve by Simplex Method

Maximize Z= 6x + 8y

Subject to,

5x + 10y<=60

4x + 4y <=40

Where x,y >=0

19. What are the important characteristics of OR? Explain the phases of solving a problem using Operations Research?

Section – C

III) Compulsory Question                                                                                          (1 X 20=20)

1. IV) The following details of a project are known.
2. Draw the network diagram     (4)
3. Find the expected time and variance of activities.   (3)
4. Find the earliest and latest starting and finishing time of each activity.(4)
5. Find total float, free float and independent float of all non critical activities.(3)
6. Identify the critical path and the project duration? (2)

 

1. What is the probability that the project may be completed in (3)
2. i) 25 days ii) 20 days    iii) 30 days
3. g) If you want to be 99% sure of completing the project what should be the deadline? (1)

 

Activity	To	Tm	Tp
1-2	3	6	15
1-3	2	5	14
1-4	6	12	30
2-5	2	5	8
2-6	5	11	17
3-6	3	6	15
4-7	3	9	27
5-7	1	4	7
6-7	2	5	8

 

 

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