st. joseph’s college of commerce (autonomous)

END SEMESTER EXAMINATION – MARCH/APRIL 2015

b.com – vi semester

C1 11 602: OPERATION RESEARCH

Duration: 3 Hours Max. Marks: 100

SECTION – A

Answer ALL the questions. Each carries 2 marks. (10×2=20)

What is Operation Research?

Explain symbolic models and mention the two types of symbolic models with suitable examples.

Introduce suitable slack, surplus or artificial variables for the expressions:

(a) 2x + 5y = 6

(b) 450a + 500b ≥ 1500

(d) a + b + c + d ≥ 20

How is an Unbalanced Transportation Problem different from an Unbalanced Assignment Problem? Explain.

Distinguish between CPM and PERT on any two basis.

State any four advantages of using models in O.R.

When the solution is called degenerate and non-degenerate in case of Transportation Problem? Explain.

What is a Trans-shipment Model?

Briefly bring out any two limitations of O.R.

10.

Mention the applicability of LPP in the field of Defence and Marketing.

SECTION – B

II)

Answer any FOUR questions. Each carries 5 marks. (4×5=20)

11.

Best Investment Analyst, is an investment firm that manages stock portfolios for a number of clients. A new client has just requested that the firm handle a Rs. 80,000 portfolio. The client would like to restrict the portfolio to a mix of the following two stocks:

Stock	Price per share	Estimated annual Return per share	Maximum Possible Investment
A	Rs. 50	Rs. 6	Rs. 50,000
B	Rs. 30	Rs. 4	Rs. 45,000

If ‘x’ and ‘y’ represent the number of shares of firms A and B respectively,

(a) Develop the objective function assuming that the client desires to maximize the total annual return.

(b) Write the mathematical expression for each of the following three constraints:

(i) Total investment funds available are Rs. 80,000.

(ii) Maximum investment in stock A is Rs. 50,000.

(iii)Maximum investment in stock B is Rs. 45,000.

12.

Solve the following Transportation Problem using North West Corner Method to find the IBFS.

From/To	D	E	F	Supply
A	6	4	1	50
B	3	8	7	40
C	4	4	2	60
Demand	20	95	35	?

13.

Discuss briefly the various characteristics of Operations Research.

14.

Determine the optimal assignment to minimize the total cost.

Machine/Jobs	J1	J2	J3	J4
M1	28	10	16	14
M2	4	24	12	10
M3	14	16	6	18
M4	4	8	12	20

15.

A small project consists of jobs as given in the table below:

Activity	Predecessor Activity	Duration (days)
A	—	9
B	—	8
C	—	15
D	A	5
E	B	10
F	D,E	2

(i) Draw the network.

(ii) Calculate the project duration and identify the critical path.

16.

Briefly explain the rules followed in formulating the Dual of a given LPP.

SECTION – C

III)

Answer any THREE questions. Each carries 15 marks. (3×15=45)

17.

Solve the following LPP using Simplex Method.

Objective function:

Maximize Z = 1000x + 4000y + 5000 z

Subject to Constraints:

3x + 3z ≤ 22

x + 2y + 3z ≤ 14

3x + 2y ≤ 14

Where x, y and z ≥0

18.

(a) Briefly explain ANY SIX Techniques of Operations Research in Business with suitable examples. (12 marks)

(b) Write short notes for the following terms:

(i) Feasible solution (ii) Network (iii) Non-Negativity Restriction (3 marks)

19.

A company has four sales representatives who are assigned to four different sales territories. The monthly sales increase estimated for each sales representative for different sales territories (in lakhs of rupees) are shown in the following table:

Sales Representatives/ Sales Territories	I	II	III	IV
A	200	150	170	220
B	160	120	150	140
C	190	195	190	200
D	180	175	160	190

Suggest an optimal assignment and the total maximum sales increase per month. If for certain reasons sales representative ‘B’ wants only sales territory III, will the optimal assignment schedule be different? If so find that schedule and the effect on the total sales.

20.

A manufacturer has distribution centres located at Agra, Allahabad and Guwahati. These centres have available 40, 20 and 40 units of his product respectively. His retail outlets require the following number of units:

Patna = 25; Varanasi = 10; Silchar = 20; Kolkata = 30 and Kanpur = 15.

The shipping cost per unit in Rs. Between each centre and outlet is given in the table below:

Distribution Centre	Retail Outlets
Distribution Centre	Patna	Varanasi	Silchar	Kolkata	Kanpur
Agra	55	30	40	50	50
Allahabad	35	30	100	45	60
Guwahati	40	60	95	35	30

(i) Determine the shipping cost using VAM (only IBFS). (7 marks)

(ii) If the problem is solved using NWCM and LCM will the IBFS of shipping cost vary? If yes, show the changes. (7 marks)

(iii) Of all the three methods of IBFS which method is most preferred and why? (1 mark)

21.

Use the graphical method to solve the following LPP.

Maximize Z = 80 a + 120 b

Subject to constraints:

a + b ≤ 9

a ≥ 2

b ≥ 3

20a + 50 b ≤ 360

where, a , b ≥ 0

SECTION – D

IV)

Case Study (1×15=15)

22.

A project is composed of the following activities, whose time estimates are listed in the table below:

Activity	Estimated duration (weeks)
Activity	Optimistic (to)	Most Likely ™	Pessimistic (tp)
1-2	1	1	7
1-3	1	4	7
2-4	2	2	8
2-5	1	1	1
3-5	2	5	14
4-6	2	5	8
5-6	3	6	15

You are required to:

a. Draw the project network and find the expected project length and the critical path. (6 marks)

b. Find the variance and standard deviation of the project on the critical activities. (2 marks)

c. Calculate earliest and latest time occurrence and total float for each activity. (4 marks)

d. What is the probability that the project will be completed within 21 weeks? (1.5 marks)

e. Suppose the manager wants 85% surety, when should he start the project? (1.5 marks)

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