Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Winter 6th Sem Old 161601 Modelling Simulation And Operations Research Previous Question Paper
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ? VI (Old) EXAMINATION ? WINTER 2019
Subject Code: 161601 Date: 16/12/2019
Subject Name: Modelling Simulation And Operations 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) Explain Simulation with real life examples? 07
(b) What is operation research? Explain different phases of OR? 07
Q.2 (a) List the various replacement policies? Explain all with suitable example? 07
(b) Explain simplex and Dual method with example? 07
OR
(b) Consider the production planning of the Super Fast Manufacturing Company
which makes items P and V. The Steel requirement for P is 400gm per piece and
that for V is 350gm per piece. Both P and V, are machined on Lathe which takes
85 and 50 minutes respectively, and are processed on a Grinder which requires
55 and 30 minutes respectively. Each unit of P consumes 20 minutes of Polishing
time. The resource availability is: Total Machine Time is 1,450 hours and Total
Steel is 250 kg. 30% of total machine time is that of Lathe, 50% of grinder and
the remaining of polishing. Unit contribution to profits for P and V is Rs 40 and
Rs 30 respectively. Formulate this as a Linear Programming model for
determining the number of units of P and V to be produced which would
maximize the profits. Given also is the constraints that the company cannot sell
more units of item P than of item V.
07
Q.3 (a) A retired person wants to invest upto an amount of Rs 30,000 in fixed income
securities. His broker recommends investing in two bonds: Bond A yielding 7%
and Bond B yielding 10%. After some consideration, he decided to invest at most
Rs 12,000 in Bond B and at least Rs 6,000 in Bond A. He also wants the amount
invested in Bond A to be at least equal to the amount invested in Bond B. what
should the broker recommend if the investor wants to maximize his return on
investment? Solve graphically?
07
(b) Solve the following LPP :
Maximize Z=6 P + 20 Q
Subject to, 2 P + Q ? 32
3 P + 4 Q ? 80
P ? 8
Q ? 10
07
OR
Q.3 (a) Explain CPM and PERT with suitable example? 07
(b) What is Queuing system? Analyse hospital system as queuing system? 07
Q.4 (a) Write the dual of the following LPP:
Minimise Z = 10 P + 20 Q
Subject to, 3 P + 2 Q ? 18
P + 3 Q ? 8
2 P ? Q ? 6 and P,Q ? 0
07
(b) Draw the network diagram and find critical path, earliest start and earliest finish
time of each activity of given project?
07
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ? VI (Old) EXAMINATION ? WINTER 2019
Subject Code: 161601 Date: 16/12/2019
Subject Name: Modelling Simulation And Operations 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) Explain Simulation with real life examples? 07
(b) What is operation research? Explain different phases of OR? 07
Q.2 (a) List the various replacement policies? Explain all with suitable example? 07
(b) Explain simplex and Dual method with example? 07
OR
(b) Consider the production planning of the Super Fast Manufacturing Company
which makes items P and V. The Steel requirement for P is 400gm per piece and
that for V is 350gm per piece. Both P and V, are machined on Lathe which takes
85 and 50 minutes respectively, and are processed on a Grinder which requires
55 and 30 minutes respectively. Each unit of P consumes 20 minutes of Polishing
time. The resource availability is: Total Machine Time is 1,450 hours and Total
Steel is 250 kg. 30% of total machine time is that of Lathe, 50% of grinder and
the remaining of polishing. Unit contribution to profits for P and V is Rs 40 and
Rs 30 respectively. Formulate this as a Linear Programming model for
determining the number of units of P and V to be produced which would
maximize the profits. Given also is the constraints that the company cannot sell
more units of item P than of item V.
07
Q.3 (a) A retired person wants to invest upto an amount of Rs 30,000 in fixed income
securities. His broker recommends investing in two bonds: Bond A yielding 7%
and Bond B yielding 10%. After some consideration, he decided to invest at most
Rs 12,000 in Bond B and at least Rs 6,000 in Bond A. He also wants the amount
invested in Bond A to be at least equal to the amount invested in Bond B. what
should the broker recommend if the investor wants to maximize his return on
investment? Solve graphically?
07
(b) Solve the following LPP :
Maximize Z=6 P + 20 Q
Subject to, 2 P + Q ? 32
3 P + 4 Q ? 80
P ? 8
Q ? 10
07
OR
Q.3 (a) Explain CPM and PERT with suitable example? 07
(b) What is Queuing system? Analyse hospital system as queuing system? 07
Q.4 (a) Write the dual of the following LPP:
Minimise Z = 10 P + 20 Q
Subject to, 3 P + 2 Q ? 18
P + 3 Q ? 8
2 P ? Q ? 6 and P,Q ? 0
07
(b) Draw the network diagram and find critical path, earliest start and earliest finish
time of each activity of given project?
07
2
Activity 1-2 1-3 1-4 2-6 3-5 4-5 4-8 5-7 6-7 7-8
Duration
(Days)
3 2 6 4 2 1 4 3 2 4
OR
Q.4 (a) What is Monte Carlo simulation? Write advantages and disadvantages of
simulation?
07
(b) Solve the following problem using North-West Corner transportation method.
To: P Q R S Supply
From A: 12 10 12 13 500
From B: 7 11 8 14 300
From C: 6 16 11 7 200
Demand 180 150 350 320 1000
07
Q.5 (a) Determine the optimum replacement interval of an equipment which costs of Rs
5,200 and whose resale values and running costs are as follows:
Year 1 2 3 4 5 6 7
Resale
Values
3,500 2,700 1,800 1,000 850 600 425
Running
Cost
600 850 1,000 1,250 1,400 1,475 2,000
07
(b) What is replacement problem? Describe some important replacement situations
and policies?
07
OR
Q.5 (a) Explain Lease Cost method with suitable example. 07
(b) Solve the following problem with Hungarian assignment method:
S1 S2 S3 S4 S5
B1 4 6 7 5 11
B2 7 3 6 9 5
B3 8 5 4 6 9
B4 9 12 7 11 10
B5 7 5 9 8 11
07
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This post was last modified on 20 February 2020