Questions
Syllabus
Qns. By Syllabus

Semester

Subject

Year

Tribhuwan University

Institute of Science and Technology

Model

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.

$\text{Max. } Z = 10 X_1 + 20 X_2$

$4X_1 + 2X_2 \leq 60$

$4X_1 + 10X_2 \leq 100$

$2X_1 + 3X_2 \leq 38$

$X_1,\, X_2 \geq 0$
[10]
2.
Find the optimum transportation schedule from the following data in order to minimize transportation costs by using modified distribution method.

$\begin{array}{|c|c|c|c|c|c|}\hline \text{Plant} & X & Y & Z & \text{Supply (units)} & \\ \hline A & 5 & 2 & 8 & 150 & \\ B & 4 & 3 & 5 & 150 & \\ C & 2 & 4 & - & 200 & \\ D & 6 & 3 & 4 & 250 & \\ \hline \text{Demand (units)} & 250 & 200 & 175 & \frac{750}{625} & \\ \hline \end{array}$
[10]
3.
The following activities must be completed in order to complete the project. Determine the critical path and time duration of the project based slack time of the activity.

$\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}\hline \text{Activity} & A & B & C & D & E & F & G & H & I & J \\ \hline \text{Predecessor} & - & - & A, B & B & A & C & E, F & D, F & G, H & I \\ \hline \text{Time (in days)} & 3 & 8 & 4 & 2 & 1 & 7 & 5 & 6 & 8 & 9 \\ \hline \end{array}$
[10]
Section B

Short Answers Questions

Attempt any Eight questions.
[8*5=40]
4.
A work project consists of twelve activities labeled through L. Upon being asked to specify the order in which the jobs had to be done, the manager answered as follows: A, B, and C are the first activities of the project and can start simultaneously and immediately; A and B precede D while B precede E, F and H. Activities F and C precede G while E and H precede I and J. The activities C, D, F and J precede K which, in turn, precedes L. Further I, G and L are the terminal activities of the project. Draw a network diagram corresponding to the project. [5]
5.
A marketing manager has four salesmen and four sales districts. Considering the capabilities of the salesmen and nature of districts, the marketing manager estimates that sales per month in hundreds of rupees for each salesman in each district would be as follows: Make the use of Hungarian method to assign the salesmen in different districts in such a way that total sales would be maximized.

$\begin{array}{|c|c|c|c|c|}\hline \text{Sales} & A & B & C & D \\ \hline P & 32 & 38 & 40 & 28 \\ Q & 40 & 24 & 28 & 21 \\ R & 41 & 27 & 33 & 30 \\ S & 22 & 38 & 41 & 36 \\ \hline \end{array}$
[5]
6.
The following table gives the payoff in million in the competitive situation between Nepal Telecom Communication (NTC) and Ncell. Determine the optimal strategies for each of the company and find the game value.

$\begin{array}{|c|c|c|c|}\hline \text{NTC$\backslash$Ncell} & \text{No Adv} & \text{Med Adv} & \text{High Adv} \\ \hline \text{No Adv} & 50 & 40 & 28 \\ \text{Med Adv} & 70 & 50 & 45 \\ \text{High Adv} & 75 & 52 & 50 \\ \hline \end{array}$
[5]
7.
An airlines organization has one reservation clerk on duty in its local branch at any given time. The clerk handles information regarding passenger reservations and flight timing. Assume that the number of customers arriving during any given period is Poisson distributed with an arrival rate of eight per hour and that the reservation clerk can service a customer in six minutes on an average, with an exponentially distributed service time. (a) What is the probability that the system is busy? (b) What is the average time a customer spends in the system? [5]
8.
A newspaper boy estimates the probability of the demand for a new magazine is as follows: A copy of the magazine cost of Rs. 8 can be sold for Rs. 10. Based on this information, find optimal number of the newspaper that would maximize the profit by using marginal analysis approach.

$\begin{array}{|c|c|c|c|c|c|c|}\hline \text{Demand} & 11 & 12 & 13 & 14 & 15 \\ \hline \text{Probability} & 0.10 & 0.15 & 0.30 & 0.25 & 0.20 \\ \hline \end{array}$
[5]
9.
The XYZ Company combines factors A and B to form a product which must weigh 50 pounds. At least 20 pounds of A and no more than 40 pounds of B can be used. The cost of A is Rs. 25 per pound and of B is Rs. 10 per pound. Formulate LPP to find the amount of factor A and B which should be used to minimize the cost. [5]
10.
What is called a game in a competitive market? State the assumptions underlying in game theory. [5]
11.
What is called a queue? Describe the operating characteristics of the single channel queuing model. [5]
12.
Write short notes on: a. Importance of Operation research on objective optimization Write short notes on: b. Dominance Rule Method in game theory [2.5+2.5]