Questions
Syllabus
Qns. By Syllabus

Semester

Subject

Year

Tribhuwan University

Institute of Science and Technology

2079

Bachelor Level / Second Year / Fourth Semester / Science

Bachelors in Information Technology (ORS255)

(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 Answers Questions

Attempt any TWO questions.
[2*10=20]
1.
Solve the given Linear Programming Problem (LPP) by using simplex method and interpret the results.

$Minimize Z=25A+10B$

$\text{subject to constraints:}$

$A+B=50$

$A \geq 20$

$B \leq 40$

$Where A,B \leq 0$
[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 given in the table.

$\begin{array}{|c|c|c|c|c|}\hline & \text{A} & \text{B} & \text{C} & \text{Units demanded} \\ \hline X & 9 & 10 & 10 & 5 \\ Y & 10 & 14 & 8 & 20 \\ Z & 13 & 10 & 8 & 20 \\ \hline \text{Units available} & 20 & 15 & 10 & 45 \\ \hline \end{array}$
[10]
3.
The table below gives the information about the activities, their predecessors and time duration required to complete the activities of the project. Draw the network diagram and identify the critical activities and critical path. Also find the minimum time duration required to complete the project.

$\begin{array}{|c|c|c|c|c|c|c|c|c|}\hline \text{Activity} & A & B & C & D & E & F & G & H \\ \hline \text{Predecessor} & - & - & A & B & A,D & B & C,E,F & G \\ \hline \text{Time in weeks} & 5 & 12 & 6 & 3 & 2 & 6 & 14 & 22 \\ \hline \end{array}$
[10]
Section B

Short Answers Questions

Attempt any Eight questions.
[8*5=40]
4.
Kathmandu 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. Four individuals have made the following bids (in thousands Rs.). Make the use of Hungarian method to assign the individuals to different motorbike company in order to maximize the revenue.

$\begin{array}{|c|c|c|c|c|}\hline \text{Individuals} & \text{Honda} & \text{Hero} & \text{Bajaj} & \text{Yamaha} \\ \hline A & 100 & 90 & 110 & 90 \\ B & 110 & 100 & 95 & 95 \\ C & 105 & 95 & 90 & 105 \\ D & 115 & 100 & 95 & 100 \\ \hline \end{array}$
[10]
5.
A milk salesman estimates the probability of the demand for a litre of milk is as follows: He purchases 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.

$\begin{array}{|c|c|c|c|c|c|c|}\hline \text{Demand} & 11 & 12 & 13 & 14 & 15 \\ \hline \text{Probability} & 0.10 & 0.15 & 0.30 & 0.25 & 0.20 \\ \hline \end{array}$
[5]
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 satisfies all the conditions for apply queuing theory, find the average (expected) queue length and the waiting time for the patient to be served. [5]
7.
Determine the best strategy for each players A and B and value of the game.

$\begin{array}{|c|c|c|c|c|}\hline \text{PlayerA/PlayerB} & B_1 & B_2 & B_3 & B_4 \\ \hline A_1 & 40 & 40 & 40 & 40 \\ A_2 & 30 & 30 & 20 & 50 \\ A_3 & 10 & 30 & 90 & 20 \\ \hline \end{array}$
[5]
8.
The following tables gives the three kinds of foods and three kinds of vitamin contained on them. Formulate objective function and constraints of LPP for minimizing the cost.

$\begin{array}{|c|c|c|c|c|}\hline \text{Vitamin} & F_1 & F_2 & F_3 & \text{Daily Requirements} \\ \hline V_1 & 20 & 10 & 10 & 300 \\ V_2 & 10 & 10 & 10 & 200 \\ V_3 & 10 & 20 & 10 & 240 \\ \hline \text{Cost per unit of food} & \text{Rs. 20} & \text{Rs. 24} & \text{Rs. 18} & \\ \hline \end{array}$
[5]
9.
Describe modified distribution (MODI) method used for testing the optimality of initial solution of transport problem. [5]
10.
What is called a queue? Describe the operating characteristics of the single channel queuing model. [5]
11.
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.

$\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}\hline \text{Activity} & P & Q & R & S & T & U & V & W & X \\ \hline \text{Predecessor} & - & - & P, Q & Q & P & R & T, U & S, U & V, W \\ \hline \end{array}$
[5]
12.
Write short note on: a. Scopes of operations research Write short note on: b. Dominance Rule Method in game theory [2.5+2.5]