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BIT Operations Research

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BIT Semester 4 Operations Research Question Paper 2079 – Solved

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Institute of Science and Technology

2079

Bachelor in Information Technology

Operations Research

ORS255

Full Marks: 60

Pass Marks: 24

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

"Section A"

Long Answer Questions Attempt any TWO questions.

[2 × 10 = 20]

1.

Solve the given Linear Programming Problem (LPP) by using simplex method and interpret the results.

Minimize \(Z = 25A + 10B\)

Subject to constraints:

\(A + B = 50\)

\(A \geq 20\)

\(B \leq 40\)

Where, \(A, B \leq 0\)

[10]
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 give in the table.

To \ From A B C Units demanded
X 9 10 10 5
Y 10 14 8 20
Z 13 10 8 20
Units available 20 15 10 45 / 45
[10]
3.

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

Activity A B C D E F G H
Predecessor - - A B A,D B C,E,F G
Time in weeks 5 12 6 3 2 6 14 22

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

[10]

"Section B"

Short Answer Questions Attempt any EIGHT questions.

[8 × 5 = 40]

1.

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

Individuals Motorbike Company
Honda Hero Bajaj Yamaha
A 100 90 110 90
B 110 100 95 95
C 105 95 90 105
D 115 100 95 100

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

[5]
2.

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

Demand 11 12 13 14 15
Probability 0.10 0.15 0.30 0.25 0.20

He purchase a litre of milk @ of Rs. 60 and sells it @ of Rs. 70. Prepare payoff table and find optimum stock by using EMV criteria assuming the unsold milk has no scrap value.

[5]
3.

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

[5]
4.

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

Player A’s strategy Player B’s startegy
\(B_1\) \(B_2\) \(B_3\) \(B_4\)
\(A_1\) 40 40 40 40
\(A_2\) 30 30 20 50
\(A_3\) 10 30 90 20
[5]
5.

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

Vitamin Food Daily Requirements
\(F_1\) \(F_2\) \(F_3\)
\(V_1\) 20 10 10 300
\(V_2\) 10 10 10 200
\(V_3\) 10 20 10 240
Cost per unit of food Rs. 20 Rs. 24 Rs. 18
[5]
6.

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

[5]
7.

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

[5]
8.

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

Activity P Q R S T U V W X
Prececessor - - P, Q Q P R T, U S, U V, W
[5]
9.

Write short note on:

a. Scopes of operations research

b. Dominance Rule Method in game theory

[2.5 × 2 = 5]