Seat No.
: ________ Enrolment
No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
MBA - SEMESTER–II • EXAMINATION – SUMMER 2013
Subject Code: 2820007 Date: 27-05-2013
Subject Name: Quantitative Analysis - II
Time: 10:30am – 01:30pm Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a) Define quantitative analysis and explain quantitative analysis approach. 07
(b) The Electrocomp Corporation manufacturers’ two electrical products: air 07
conditioners and large fans. The assembly process for each is similar in
that both require a certain amount of wiring and drilling. Each air
conditioner takes 3 hours of wiring and 2 hours of drilling. Each fan must
go through 2 hours of wiring and 1 hour of drilling. During the next
production period, 240 hours of wiring time are available and up to 140
hours of drilling time may be used. Each air conditioner sold yields a
profit of Rs. 25. Each fan assembled may be sold for Rs. 15 profit.
Formulate and solve this LP production mix situation to find the best
combination of air conditioners and fans that yields the highest profit.
Solve the problem by using graphical method.
Q.2 (a) Write the dual of the following linear programming problems: 07
(a) Maximize Z=10Y1 + 8Y2 – 6Y3
Subject to
3Y1 + Y2 – 2Y3 ≤ 10
-2Y1 + 3Y2 – Y3 ≥ 12
Y1,Y2,Y3 ≥ 0
(b) Minimize Z= -4X1 + 3X2
Subject to
X1 - 2X2 ≤ -4
2X1 + 3X2 ≥ 13
-X1 + X2 ≤ -4
X1, X2 ≥ 0
(b) Define and explain sensitivity analysis. 07
OR
(b) Define and explain goal programming problems. 07
1
Q.3 (a) A salesman has to visit five cities A, B, C, D and E, starting from his 07
home city A and back to home city A. The inter-city distance are given as
follows:
To
From A B C D E
A -- 220 210 230 190
B 220 -- 230 200 210
C 210 230 -- 240 220
D 230 200 240 -- 230
E 190 210 220 230 --
How should the salesman plan his tour so that the total distance travelled
by him is the minimum?
(b) A firm owns facilities at six places. It has manufacturing plants at places 07
A, B and C with daily production of 50, 40 and 60 units respectively. At
point D, E and F it has three warehouses with demands of 20, 95 and 35
units respectively. Per unit shipping costs are given in the following table.
If the firm wants to minimize its total transportation cost, how should it
route its products?
Warehouse
D E F
A 6 4 1
Plant B 3 8 7
C 4 4 2
Find the initial feasible solution by using N/W corner method, Least cost
method and VAM method.
OR
Q.3 (a) The following information is available regarding four different jobs to be 07
performed and about the clerks capable of performing jobs:
Jobs (Time taken in hours)
A B C D
I 4 7 5 6
II -- 8 7 4
Clerks
III 3 -- 5 3
IV 6 6 4 2
Clerks II cannot be assigned to job A and clerk III cannot be assigned to
job B. You are required to find out the optimal assignment schedule and
the total time taken to perform the jobs. Also find whether the given
problem has more than one optimal assignment schedule.
2
(b) A company has three plants and four warehouses. The supply and demand 07
in units and the corresponding transportation costs are given.
Below table shows initial solution of problem.
Warehouses
I II III IV
Plants Supply
10
1
5 10 4 5 10
20 5
2
6 8 7 2 25
5 10 5
3
4 2 5 7 20
Demand 25 10 15 5 55
Answer the following questions, giving brief reasons:
(a) Is this solution feasible?
(b) Is this solution degenerate?
(c) Is this solution optimal?
(d) Does this problem have more than one optimal solution? If so,
show all of them.
Q.4 (a) A new shopping mall is considering setting up an information desk 07
manned by one employee. Based on information obtained from similar
information desks, it is believed that people will arrive at the desk at the
rate of 20 per hour. It takes an average of 2 minutes to answer a question.
It is assumed that arrivals are Poisson and answer times are exponentially
distributed.
(a) Find the probability that the employee is idle.
(b) Find the proportion of the time that the employee is busy.
(c) Find the average number of people receiving and waiting to
receive information.
(d) Find the average number of people waiting in line to get
information.
(e) Find the average time person seeking information spends at the
desk.
(f) Find the expected time a person spends just waiting in line to
have a question answered.
(b) What is Markov analysis? List the assumptions that are made in Markov 07
analysis.
OR
Q.4 (a) What is simulation? What are the advantages and limitations of 07
simulation?
3
(b) A Bajaj company manufactures around 150 bikes. Depending upon the 07
availability of raw materials and other conditions, the daily production has
been varying from 146 bikes to 154 bikes, whose probability distribution
is as given below:
Production/day Probability
146 0.04
147 0.09
148 0.12
149 0.14
150 0.11
151 0.10
152 0.20
153 0.12
154 0.08
The finished bikes are transported in a specially designed lorry that can
accommodate only 150 bikes. Using following random numbers 80, 81,
76, 75, 64, 43, 18, 26, 10, 12, 65, 68, 69, 61, 57 stimulate the process to
find out
(a) What will be the average number of bikes waiting in the factory?
(b) What will be the average number of empty space on the lorry?
Q.5 (a) Hal has enough clay to make 24 small vases or 6 large vases. He only has 07
enough of a special glazing compound to glaze 16 of the small vases or 8
of the large vases. Let X1 = the number of small vases and X2 = the
number of large vases. The smaller vases sell for Rs.3 each, while the
larger vases would bring Rs.9 each.
Formulate the problem as linear programming problem.
(b) What is integer programming? List down three types of integer 07
programming problems.
OR
Q.5 (a) What is balance and unbalanced transportation problem? Describe the 07
approach you would use to solve an unbalanced problem.
(b) What is queuing problem? What are the basic characteristics of queuing 07
system?
*************
