Download AKTU (Dr. A.P.J. Abdul Kalam Technical University (AKTU), formerly Uttar Pradesh Technical University (UPTU) B-Tech 8th Semester (Eight Semester) 2015-16 051 EME 051 Operations Research Question Paper
(Following Paper 1]) and Roll N o. to be ?lled in your
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B. TECH.
Theory Examination (Semester-Vlll) 2015-16
OPERATIONS RESEARCH
Time : 3 Hours Max. Marks : 100
Section-A
1. Attempt all parts. All parts carry equal marks. Write
answer of each part in short. (ZXIO=20)
(3) Discuss simplex and convex set with respect to LPP.
(b) Explain the concept of alternate optima in LPP.
(c) What is degeneracy in TP?
((1) What is curse of dimensionality?
(e) Why we use dominance property?
(1) How can we solve problems with risk?
(g) What are different techniques of selective inventory
control?
(b) When we need simulation?
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(i) Explain balking in queue.
(i) What do you understand by crashing of resources?
Section-B
Attempt any ?ve questions from this section.
(10XS=50)
(a) Solve the given LPP model by simplex method:
Max Z = 3xl + 2x2
Subject to,
2xI + x2 S 2
3x1 + 4x2 2 12
x1, x2 2 0
(b) Obtain optimal solution of the transportation prob-
lem given below :
D1 D2 D3 D1 Supply
Fl 2 2 2 l 3
F2 10 8 5 4 7
F3 7 6 6 8 5
Demand 3 4 4
(c) With help of an example, explain the Hungarian
algorithm
(2)
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(d)
(e)
(f)
(g)
Solve the game given below for the two players A and
B:
Player B
Player A 1 3 1 l
8 5 2
A company has six jobs. each of which has to pass
through two machines MI and M2 for processing.
The processing time for the jobs on each machine
(in hours) is given below:
Job A B c D E F
MI 1 4 6 3 5 2
M 3 6 8 8 1 5
2
Find optimum sequence, total elapsed time as well
as idle times for the two machines.
A contractor has to supply 10,000 bearings per day
to an automobile manu?wturer. He ?nds that when
he starts production run, he can produce 25,000
bearings per day. The holding cost of a bearing in
stock in Rs 0.02 per year. Set-up cost of a produc-
tion is Rs 18. How ?'equently should the production
run be made?
A car par contains 5 cars. The an?ival of cars is
Poisson with mean of 10 per hour. The length of
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time each car spends in the car park is exponential With Subject to,
mean of 0.5 hour. How many cats are in the car park
x + + = 22
on an average? ? x2 x3
3xl+5x2?2x3365
(h) Con51der the followmg pl'OJCCt : g X] + 7x2 _ 4x3 2 120
Activity Player B x1, x2 2 0 and x1 is unrestricted. (5)
t? t? (b) A soft drink distnbutor takes the contract for the sale of
A 3 6 soft dn'nks at a cricket stadium during a one day match.
B 2 5 He has 5 sales boys to assign to three areas of the
C 2 4 stadium. The table below, shows estirmted sales that can
D 2 3 be nude with di??erent assignments:
E 1 3
F 4 6 No of salesmen East stand North stand Club stand
G 1 5 assigned
1 15 45 30
Draw the network and ?nd the critical path and 2 30 90 60
van'ances. Also ?nd the probability of completing the 3 60 135 90
project by 18 weeks.
4 120 180 120
5 150 180 150
Sec?on?C
Use dynamic programming to obtain assignment of sales-
Note : Attempt any two questions from this section. men for sales . . ion (10)
(15x2=3o)
4. (a) Explain the procedure for sequencing 2 jobs on k
3. (a) Make dual of the following primal model : ; machines. (5)
MinZ=4xl+5x2?3x3
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(b)
00
Use dual simplex method to solve the LPP model given
below: (10)
Max Z = 3x1 ? x2
Subject to, Xl + X2 2 1
2x1 + 3x2 2 2
x1, x2 2 0
What do you understand by simulation? Discuss
different methods for generation of rando numbers.
(5)
The demand for a certain product has a rectangular dis?
tribution between 4000 and 5000. Find the optimal
order quantity, if the storage cost is Rs 1 per unit and
shortage cost is Rs 7 per unit. (10)
(6)
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This post was last modified on 29 January 2020