BIT 4th Semester
Operations Research Question Paper 2079

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ORS 255-2079 ✡
Tribhuvan University
Institute of Science and Technology
2079
✡
Bachelor Level/Second Year/Fourth Semester/Science
Bachelors in Information Technology (ORS 255)
(Operations Research)
Full Marks:60 Pass Marks:24 Time:3 hours

Candidates are required to give their answers in their own words as for as practicable.
The figures in the margin indicate full marks

Section A
Long Answer Questions
Attempt any Two question.
[2x10=20]
1.

Solve the given Linear Programming Problem (LPP) by using simplex method and interpret the results.
Minimize Z = 2A + 10B
Subject to constraints:
A + B = 50
A ≥ 20
B ≤ 40
Where, A, B ≥ 0

2.

Find transport schedule to minimize the transportation cost for the following transportation problem. The transportation cost per unit and units demanded and available are given in the table.

FromToABCUnits demanded
X910105
Y1014820
Z1310820
Units available20151045

3.

The table give below give the information about the activities, their predecessors and time duration required to complete the activities of the project.

ActivityABCDEFGH
Predecessor--ABA,DBC,E,FG
Time in weeks51263261422

Draw the network diagram and identify the critical activities and critical path. Also find the minimum time duration required to complete the project.

Section B

Attempt any Eight questions

[8x5=40]
4.

Callennoids Metropolitan is putting up bids for four used motorbikes company. The Metropolitan allows individuals to make bids on all four motorbikes company but will accept only one bid per individual have made the following bids (in thousands Rs).

Motorbike Company
IndividualsHondaHeroBajajYamaha
A1009011090
B1101009595
C1059590105
D11510095100

Make the use of Hungarain method to assign the individuals to different motorbike company in order to maximize the revenue.

5.

A milk salesman estimates the probability of the demand for a litre of milk is as follows:

Demand1112131415
Probability0.100.150.300.250.20

He purchase a litre of milk @ of Rs. 60 and sells it @ of Rs. 70. Prepare payoff table and find the optimal act based on using EMV and EOL criterion determining the unsold milk has value.

6.

On the average 96 patients per 24 hours day require the emergency service in clinic. Also on the average, a patient requires 10 minutes of active attention. Assume that the facility can handle only one emergency at a time. If this situation satisfy the all the conditions for apply queuing theory, find the average (expected) queue length and the waiting time for the patient to be served.

7.

Determine the best strategy for each player A and B and value of the game.

Player A's strategy:Player B's strategy:
B₁B₂B₃B₄
A₁40404040
A₂30302050
A₃10309020

8.

The following tables gives the three kinds of foods and three kinds of vitamin contained on them. Formulate objective function and constraint of LPP for minimizing the cost.

VitaminFoodDaily Requirements
F₁F₂F₃
V₁201010300
V₂101010200
V₃102010240
Cost per unit of foodRs. 20Rs. 24Rs. 18

9.

Describe modified distribution (MODI) method used for testing the optimality of initial solution of transport problem.

10.

What is called a queue? Describe the operating characteristics of the single channel queuing model.

11.

The following activities must be completed in order to complete the project. Draw network diagram and establish relationship between the activities of the project.

ActivityPQRSTUVWX
Predecessor--P, QQPRT, US, UV, W

12.

Write short note on:
a. Scopes of operations research
b. Dominance Rule Method in game theory