DU SOL M.Com Question Paper 1st Year 2018 Sem 2 Quantitative Techniques For Business Decisions

This question paper contains 4+1 printed pagesl

Your Role Number

4t43

M. Com. : Semester-Il (OC) G

Paper No. 6203

QUANTITIT|IVE TECHNIQUES FOR BUSINESS DECISIONS

Timp: 3 Hours MaximumMarks: 100

(Yy'rite your Roll No. on the top immediately on receipt of this question
paper.)

Attempt any five questions.

All questions carry equal marks.
l. A firm is engaged in producing two products : Pl and P2. The relevant data are given
here:

P1 Y2

SP/unit Rs. 200 Rs. 240
Direct Material Rs. 45 Rs. 50
Direct wages : 8 hrs @ Rs. 2ftrr l0 hrs @ Rs. 2lhr
Deptt A l0 hrs @ Rs. 2.25fttr 6 hrs @ Rs. 2.25lhr
Deptt B 4 brs @ Rs. 2.5/tr 12 hrs @ Rs. 2.5/hr
Deptt C

Variable overheads Rs. 6.50 Rs. I 1.50
o Fixed overheads Rs. 2,85,000 per annum

o No. of employees in A, B and c departments are 20, 15, lg respectively

P.T.O.

(2) 4143

. No. of hrs/employee/week = 40 in each department

o No. of weeks per annum = 50

(, Formulate it as LPP
(ii) Solve graphically
(iii) Determine product mix
(iv) Determine amount of profit and contribution per year
(v) Do you observe any redundant constraint ? If yes, which one ? 20

2. A manufacturing company makes three products, each of which requires three operations as
part of the manufacturing process. the company can sell all of the products it can manufacture
but its production capability is limited by the capacity of its operation centres.

Additional data conceming the company are as follows :

Prnduct Manufacturing requirement (hrs/unit)

Centre Centre Centre Cost Selling price

I 2 J (Rs.) (Rs.)

A I a
J 2 ll l5

B 5 4 1 12 20

C 2 2 2 10 r6

Hours available 160 t20 80

(,) What is the optimal product mix ? What is the maximum profit ?

(ii) What are the shadow prices of the resources ? Which resource has highest marginal
value ?

(iii) Over what range in each of RHS valueso are these shadow prices valid ?
(tv) Ranges over which the objective function coefficients can vary for each of the decision
variables ?

(v) State the dual to this problem and write its solution. 20

(r) 4t43

Stronghold Construction Company is interested in taking loans from banks for some of
a its
J.

projects, p, R, S, T. The rates of interest and the lending capacity differs from bank to
e,
bank. All these projects are to be completed. The relevant details are provided in the following
table.Assuming the role of a consultant advice this company as to how this should take the
loans so that the total interest payable will be the least. fue there any altemate optimum
solutions ?
20
If so, indicated one such solution ?
Bank Interest Rate in Percentage for Project Maximum Credit

P a R S T (in thousands)

Private Bank 20 l8 t8 t7 t7 Any Amount

Nationalized 16 l6 l6 i5 t6 400

Cooperative Bank 15 15 15 13 14 250

Amount Required 200 r50 200 t25 /)
(in thousands)

4. Activity Immediately Normal Normal Crash Crash

Preceding Time Cost (Rs.) Time Cost (Rs.)

Activity (Days) (Days)

A J 140 2 210

B 6 215 5 275

C 2 160
1
I 244
a
D A 4 130 J 180

E A 2 170 I 250

F A 165 4 205

G B,D 4 210 J 290

H C,E 3 110 2 160
P.T.O.

(4) 4t43

(t) Draw a PERT network.

(ii) Find out the critical path and the expected project completion date.

(iiil What is the minimum possible project completion time after crashing the activities and
the associated cost of completing the project ? 20

5. A dispatcher of the police department has received four requests for police assistance. Currently,

six patrol cars are available for assignment and the estimated response time (in minutes) are
shown in the followins table :

Patrol unit
1
Incident 2 J 4 5 6

I 6 5 5 4 5 6

-|
il 8 6 2 3 6

ilI 4 4 6 5 5

a 4
IV J 9 8

(r) Which patrol units should respond ?

(ii) What will be the average response time ? 20

6. A manufacturer of baby dolls makes two types of dolls. One is sold under the brand name
Marie and the other Suzie. Processing of these two dolls is done on two machines A and
B. The processing time for each Marie is 3 and 4 hours on machine A and B respectively,
and that of Suzie is 1 and 4 hours on machines A and B respectively. 50 hours of machine

A are available and 90 hours of machine B are available per week. The porfit contribution
for a Marie is Rs. 6 and that for Suzie is Rs. 18. Formulate and solve this problem to determine

the optimal weekly production schedule of the two dolls. (Provided an all-integer solution). 20

7. (a) Explain the basics of selective inventory control and state different selection techniques
adopted in Inventory Control System. Give a brief note on each. l0

(5) 4143
(b) A furniture dealer sells special typist chair. Each purchase order cost Rs. 50 and the
holding costs amount to Rs. 80 per chair per year. The dealer sells 90 chairs per month.
He had estimated a back-ordering cost of Rs. 20 per chair per year.

(t What is the EOQ ?

(t,) when the supply of chair comes, how many ,r,li., on an average are expected
to be delivered to the customers immediately ?

(iii) what is the total annual cost of ordering, holding and back-ordering. l0
8. (a) What is a queuing problem ? What are the basic characteristics of queuing system ? 8

(b) Arrivals at the enquiry counter of a transport company are Poisson distributed with an
average of 6 per hour. The time that the customers spend in seeking inforniation from
the clerk stationed at the counter is known to be exponentially distributed with an
averaqe
of three minutes. Using this information determine :

(r) The probability that a customer reaching the counter shall have to wait for getting

the needed information

(ii) The probability that a queue shall be formed.

(iii) The expected time that a customer shall wait in the queue to obtain information.
Suppose that the company manager employs another clerk if he is convinced
that the
customer has to wait for at least 4 minutes for receiving information. What arrival
rate
would justifr employing the second clerk ?
e

4143 5 100