Cochin University of Science and Techology (CUST) 2006 M.B.A Management Science - Question Paper

M.B.A. DEGREE (FT) II SEMESTER EXAMINATION, ] *1AY 2006

MANAGEMENT SCIENCE

MBA.F.2/06.2

Maximum marks : 50

(Answer ALL questions)

(All questions carry EQUAL marks)

(a)    Explain the steps in Decision Tree Analysis.

(b)    A news paper boy has the following probabilities of selling a magai ine:

No. of copies sold    10    U    12    13    14

Probability    0.10 0.15 0.20 0.25 0.30

Cost of copy is 30 paise and sale price is 50 paise. He cannot return unsold copies. How many copies should he order ?

OR

B. (a) Solve the game

B

19	15	-5	-2
19	15	17	16
0	20	15	5

(b) Describe how a Two-person zero-sum game can be solved by Lin :ar Programming.

II. A. Mohan Meakins Breweries Ltd. has two bottling plants, one located at S Dlan and the other at Mohan Nagar. Each plant produces three clinks whiskey, beer and fruit iuices named A, B and C respectively. The number of bottles produced per day are as follows:

Plant at

Solan (S) Mohan Nagar (M)

Whiskey    1,500    1,500

BeerB    3,000    1,000

Fruit juice C    2,000    5,000

A market survey indicates that during the month of April, there will be a demand of 20,000 bottles of whiskey, 40,000 bottles of beer and 44,000 bottles of fruit juices. The operating costs per day for plants, at Solan and Mohan Nagar are 600 and 400 monetary units. For 1 ow many days each plant be run in April so as to minimize the production cost, while still meeting the i narket demand ?

OR

B. Solve

Maximise Z = 2x, +3x₂

Subject to 6x, + 5x₂ < 25

Xj +3x₂ <10

Xj x₂ non - negatiye int

(a)    Four new machines M_1? M₂, M3 and M4 are to be installed in a nachine shop. There are five vacant places A, B, C, D and E available. Because of limited s )ace, machine M₂ cannot be placed at C and M3 cannot be placed at A. Cy the assignment cc st of machine I to place j in rupees is shown below.

A B C D E

M\

M₂

M_t

Find the optimal assignment schedule.

(b)    Distinguish between transportation model and assignment model.

OR

(a)    What are the three fundamental properties of a finite-state, first ord :r Markov chains ?

(b)    On January 1 (this year), Bakery \ had 40 per cent of its local mai ket share while the other two bakeries B and C had 40 per cert and 20 per cent, respectively, of the market share. Based upon a study by a marketing research firm, the following facts were complied. Bakery A retains 90 per cent of its customers while gaining 5 per cent of Bs customers and 10 per cent of Cs customers. Bakery B retain 85 per cent of its customers wh le gaining 5 per cent of As customers and 7 per cent of Cs customers. Bakery C retains 83 >er cent of its customers and gains 5 per cent of As customers and 10 per cent of Bs custoners. What will each firms share be on January lnext year and what will each firms market sh ire be at equilibrium ?

(a)    Write short notes on:

(i)    Traffic interning

(ii)    Service discipline and

(iii)    Queue

(b)    On average 96 patients per 24 hour day require the service of ai emergency clinic. Also an average, a patient requires 10 minutes of active attention. Assume that the facility can handle only one emergency at a time. !suppose that it costs the clinic Rs.100/- per patient treated to obtain an average servicing tims of 10 minutes, and that each minutes of decrease in this average time would cost Rs.10/- per patient treated. How much would have to be budgeted by the clinic to decrease the average size of the queue from 1V₃ patien s to Vi patient ?

OR

(a) Solve the following sequencing problem giving an optimal sclution when passing is not alldwed. Find total elapsed time corresponding to the optimal sequ ;nce.

Machine Job A B C D E Mi 11 13 9 16 17 m2 4 3 5. 2 6 m3 6 7 5 8 4 m4 15 8 13 9 11

(b) What are the general assumptions in sequencing problems.

PERT takes care of uncertain durations. How far is this stat< ment correct ? Explain with reasons.

A small project is composed of 7 activities whose time estimate; are listed in the table below. Activities are identified by their beginning (0 and ending (j) modi numbers.

Activity (H)	Estimated durations (weeks)
	Optimistic	Most likely Pessimistic
1-2	1	1	7
1-3	1	4	7
1-4	2	2	8
2-5	1	1	1
3-5	2	5	14
4-6	2	5	8
5-6	3	6	15

(i)    Draw the project network

(ii)    Find the expected duration and variance for each activity. What is the expected project length ?

(iii)    What is probability that the project will be completed at least 4 weeks earlier than expected time ?

OR

B. (a) Distinguish between solutions derived from simulation model: and solutions derived from analytical models ?

(b) A project consists of eight activities A to H. The completion tim 2 for each activity is a random variable. The data concerning probability distribution along w th completion times for each activity is as follows:

Activity	Immediate Predecessors)	Time (day) (P *obability)
		1	2	3	4	5	6	7	8	9
A				--	0.2		0.4	0.4 -
B							0.5		0.5
C	A			0.7	0.3
D	B,C		-			0.9			0.1
E	A					0.2				0.8
F	D,E				0.6	0.4
G	E			0.4	0.4		0.2	__		__
H	F	-	0.4	-	-	-	-	0.6	-

(i)    Draw the network diagram and identify the critical path.

(ii)    Simulate the project to determine the activity times. Determine the critical path and project expected completion time.

r

Attachment: cochin-university-of-science-and-techology--cust--2006-m-b-a-37399-1.pdf

Earning:   Approval pending.