STUPIDSID
1 (a)
What is Operations Research? Write its applications and also explain various
phases of Operations Research study.
7 M
1 (b)
A firm manufactures two products P1 and P2, both of which have to be
processed on two machines M1 and M2. Product P2 requires 4 hours on both
machines, while product P1 requires 6 hours on machine M1 and 2 hours on
machine M2. The available hours on machine M1 and machine M2 are 24 and
16 respectively. The profit per unit is estimated at Rs 50 for product P1 and Rs
100 for product P2. Formulate the problem and solve graphically.
7 M
2 (a)
Solve the following LPP using simplex method:
Maximize Z = 40x + 35y
subject to
2x + 3y≤ 60
4x + 3y ≤ 96
x, y≥0.
Maximize Z = 40x + 35y
subject to
2x + 3y≤ 60
4x + 3y ≤ 96
x, y≥0.
7 M
2 (b)
Solve the following LPP using two-phase method.
Minimize Z = 40x1 + 24x2
subject to:
20x1 + 50x2≥ 4800
80x1 + 50x2 ≥ 7200
x1, x2≥ 0.
Minimize Z = 40x1 + 24x2
subject to:
20x1 + 50x2≥ 4800
80x1 + 50x2 ≥ 7200
x1, x2≥ 0.
7 M
2 (c)
Obtain initial solution using Vogel's approximation method for the following
transportation problem.
| From/To | P | Q | R | S | Supply |
| A | 5 | 1 | 3 | 3 | 34 |
| B | 3 | 3 | 5 | 4 | 15 |
| C | 6 | 4 | 4 | 3 | 12 |
| D | 4 | 1 | 4 | 2 | 19 |
| Demand | 21 | 25 | 17 | 17 |
7 M
3 (a)
Briefly discuss duality in Linear Programming Problem. Write the steps to
convert a given primal problem into a dual problem. Also find dual for the
following LPP.
Maximize Z = x + 3y + 6z
subject to
3x + z ≤ 10
2x + 5y + 4z ≤ 8
x, y, z ≥ 0.
Maximize Z = x + 3y + 6z
subject to
3x + z ≤ 10
2x + 5y + 4z ≤ 8
x, y, z ≥ 0.
7 M
3 (b)
Solve the following assignment problem using Hungarian assignment method.
| Worker | Job | |||
| A | B | C | D | |
| 1 | 35 | 41 | 53 | 43 |
| 2 | 43 | 43 | 45 | 34 |
| 3 | 36 | 34 | 44 | 53 |
| 4 | 44 | 41 | 48 | 42 |
7 M
3 (c)
Briefly discuss bounded feasible region and unbounded feasible region in
graphical method of LPP. Using graphical method, state the whether the region
is bounded or not for the following LPP.
Maximize Z = 10x1 + 20x2
Subject to
2x1 + 4x2≥ 16
x1 + 5x2≥15
x1and x2≥ 0.
Maximize Z = 10x1 + 20x2
Subject to
2x1 + 4x2≥ 16
x1 + 5x2≥15
x1and x2≥ 0.
7 M
3 (d)
The ABC station has a central store where service mechanics arrive to take
spare parts for the jobs they work upon. The mechanics wait in queue if
necessary and are served on a first-come-first-served basis. The store is
manned by one attendant who can attend 16 mechanics in an hour on an
average. The arrival rate of the mechanics averages 12 per hour. Assuming that the pattern of mechanics arrivals in Poisson distributed and the servicing time is exponentially distributed. Determine the following:
(i) Utilization parameter
(ii) The probability that the given system is idle.
(iii)Expected number of mechanics in the store.
(iv) Expected number of mechanics waiting for their service.
(i) Utilization parameter
(ii) The probability that the given system is idle.
(iii)Expected number of mechanics in the store.
(iv) Expected number of mechanics waiting for their service.
7 M
4 (a)
Draw the network diagram for the following information for ten activities:
| Activity | A | B | C | D | E | F | G | H | I | J |
| Immediate | --- | ---- | B | A,B | A,B | B | E,D,F | D,E | E,F | H,G,I,C |
7 M
4 (b) (i)
Define Slack variable and artificial variable of Linear Programming
Problem with example.
2 M
4 (b) (ii)
Discuss the following special cases with respect to transportation problem:
- unbalanced problem
- prohibited route.
- unbalanced problem
- prohibited route.
5 M
4 (c) (i)
Justify the following statement: "PERT is probabilistic in nature while CPM is deterministic."
3 M
4 (c) (ii)
In the following transportation table, initial solution is given by NWC method. Find and trace closed loop for unoccupied cells (PF, QD, RD, and RE) and also find opportunity cost for the same cells.
4 M
4 (d)
What do you mean by Minimum Spanning Tree? Discuss any algorithm for
finding minimum spanning tree. Support your answer with an appropriate
Example.
7 M
5 (a)
Discuss the importance of queuing systems. Explain the types of queuing
system with the help of six-character code.
7 M
Write a brief note on :
5 (b) (i)
Random Number Generation
4 M
5 (b) (ii)
Briefly discuss maximal flow problem.
4 M
5 (c)
Discuss the term modelling and simulation in brief. Write the advantages and
disadvantages of simulation.
7 M
5 (d)
What is a replacement problem? Describe some important replacement
situation. Also discuss group replacement problem
7 M
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