Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Summer 7th Sem Old 171901 Operation Research Previous Question Paper
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER?VII (OLD) EXAMINATION ? SUMMER 2019
Subject Code: 171901 Date: 21/05/2019
Subject Name:Operation Research
Time: 02:30 PM TO 05:00 PM 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) What is OR? What are the characteristics and limitation of OR techniques? 07
(b) Solve problem by Graphical method: Maximize Z = 3X1 + 4X2;
Subjected to: 5X1 + 4X2 ? 200; 3X1 + 5X2 ? 150; 5X1 + 4X2 ? 100; 8X1 + 4X2 ?
80 ; X1 , X2 ? 0
07
Q.2 (a) Three grades of coal A, B and C contain phosphorus and ash as impurities. In a
particular industrial process, fuel up to 100 ton (maximum) is required which
should contain ash not more than 3% and phosphorous not more than 0.03%. It
is desired to maximize the profit while satisfying these conditions. There is an
unlimited supply of each grade. The percentage of impurities and the profit of
grades are given below:
Coal Phosphorous (%) Ash (%) Profit (Rs/ton)
A 0.02 3.0 12
B 0.04 2.0 15
C 0.03 5.0 14
Find the proportions in which the three grades are used.
07
(b) Explain the concept of degeneracy in Simplex method. How is it resolved? 07
OR
(b) Explain the following with reference to L.P.P.
1. Slack Variable and Surplus Variable
2. Entering Variable & Leaving Variable
07
Q.3 (a) What is degeneracy? How does the problem of degeneracy arise in a
transportation problem? How can we deal with this problem?
07
(b) Solve the following assignment problem:
I II III IV V
1 11 17 8 16 20
2 9 7 12 6 15
3 13 16 15 12 16
4 21 24 17 28 26
5 14 10 12 11 13
07
OR
Q.3 (a) What is an unbalanced assignment problem? How is the Hungarian Assignment
Method applied in respect of such a problem?
07
(b) Find the basic feasible solution of the following transportation problem by north-
west corner rule.
1 2 3 4 5 Available
A 4 3 1 2 6 80
B 5 2 3 4 5 60
C 3 5 6 3 2 40
D 2 4 4 5 3 20
Required 60 60 30 40 10
07
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER?VII (OLD) EXAMINATION ? SUMMER 2019
Subject Code: 171901 Date: 21/05/2019
Subject Name:Operation Research
Time: 02:30 PM TO 05:00 PM 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) What is OR? What are the characteristics and limitation of OR techniques? 07
(b) Solve problem by Graphical method: Maximize Z = 3X1 + 4X2;
Subjected to: 5X1 + 4X2 ? 200; 3X1 + 5X2 ? 150; 5X1 + 4X2 ? 100; 8X1 + 4X2 ?
80 ; X1 , X2 ? 0
07
Q.2 (a) Three grades of coal A, B and C contain phosphorus and ash as impurities. In a
particular industrial process, fuel up to 100 ton (maximum) is required which
should contain ash not more than 3% and phosphorous not more than 0.03%. It
is desired to maximize the profit while satisfying these conditions. There is an
unlimited supply of each grade. The percentage of impurities and the profit of
grades are given below:
Coal Phosphorous (%) Ash (%) Profit (Rs/ton)
A 0.02 3.0 12
B 0.04 2.0 15
C 0.03 5.0 14
Find the proportions in which the three grades are used.
07
(b) Explain the concept of degeneracy in Simplex method. How is it resolved? 07
OR
(b) Explain the following with reference to L.P.P.
1. Slack Variable and Surplus Variable
2. Entering Variable & Leaving Variable
07
Q.3 (a) What is degeneracy? How does the problem of degeneracy arise in a
transportation problem? How can we deal with this problem?
07
(b) Solve the following assignment problem:
I II III IV V
1 11 17 8 16 20
2 9 7 12 6 15
3 13 16 15 12 16
4 21 24 17 28 26
5 14 10 12 11 13
07
OR
Q.3 (a) What is an unbalanced assignment problem? How is the Hungarian Assignment
Method applied in respect of such a problem?
07
(b) Find the basic feasible solution of the following transportation problem by north-
west corner rule.
1 2 3 4 5 Available
A 4 3 1 2 6 80
B 5 2 3 4 5 60
C 3 5 6 3 2 40
D 2 4 4 5 3 20
Required 60 60 30 40 10
07
2
Q.4
(a)
A Branch of bank has only one typist. Since the typing work varies in length the
typing rate is randomly distributed approximating a Poisson distribution with
mean service rate of 8 letters type per hour. The letters arrive at a rate of 5 per
hour during the entire 8- hours work day. If the typewriter is valued at Rs. 1.50
per hour, determine:
a) Equipment utilization
b) The percent time that an arriving letter has to wait.
c) Average system time
d) Average cost due to waiting on the part of typewriter i.e. it remaining
idle.
07
(b) What is simulation? What are different phases of simulation process?
Differentiate between deterministic and stochastic simulation models.
07
OR
Q.4 (a)
Derive the EOQ formula
h
o
C
D C
Q
2
? Where Co = Ordering cost, D= Uniform
demand and Ch = Inventory holding cost.
07
(b) Explain the following :
a) Minimax and maximin principals
b) Two person zero sum game.
07
Q.5 (a) Explain Crashing of network. Why it is required? 07
(b) The maintenance cost and resale value per year of a machine whose purchase
price is Rs. 7000 is given below:
Year 1 2 3 4 5 6 7 8
Maintenance
cost (Rs.)
900 1200 1600 2100 2800 3700 4700 5900
Resale value
(Rs.)
4000 2000 1200 600 500 400 400 400
07
OR
Q.5 (a) Define following terms with respect to CPM/PERT :
a) Event
b) Merge event
c) Burst event,
d) activity
e) Processor activity
f) Successor activity
g) Dummy activity
07
(b) Give the difference between C.P.M and P.E.R.T 07
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This post was last modified on 20 February 2020