(AUTONOMOUS)
B. Tech VII Semester Supplementary Examinations, May 2018
(Regulations: VCE-R14)
OPERATIONS RESEARCH
(Computer Science and Engineering)
Date: 24 May, 2018 AN Time: 3 hours Max Marks: 75
Answer ONE question from each Unit
All Questions Carry Equal Marks
Unit I
1. What is operations research? List the various steps involved in OR study. 7M
Egg contains 6 units of vitamin A per gram and 7 units of vitamin B per gram and cost 12
paise per gram. Milk contains 8 units of vitamin A per gram and 12 units of vitamin B per
gram and costs 20 paise per gram. The daily requirements of vitamin A and vitamin B are
100 units and 120 units respectively. Find the optimal product mix.
8M
2. Differentiate between Deterministic and Stochastic Models. 2M
Solve by using graphical method
Maximize Z 4x1
Subject to
1 2
1
2
1 2
4 3 24
4.5
6
0
x x
x
x
x x




13M
Unit II
3. Explain the following:
i. Feasible solution
ii. Basic Feasible Solution
iii. Optimum Solution
7M
The ICARE Company has three plants located throughout a state with production
capacity 50, 75 and 25 gallons. Each day the firm must furnish its four retail shops R1, R2,
R3 and R4 with at least 20, 20, 50, and 60 gallons respectively. The transportation costs
(in Rupees) are given below. The economic problem is to distribute the available product
to different retail shops in such a way so that the total transportation cost is minimum:
Company Retail Supply
R1 R2 R3 R4
P1 3 5 7 6 50
P2 2 5 8 2 75
P3 3 6 9 2 25
Demand 20 20 50 60
8M
4. State the difference between Transportation and Assignment problems. 7M
Three jobs A B C are to be assigned to three machines X Y Z. The processing costs are as
given in the matrix shown below. Find the allocation which will minimize the overall
processing cost.
Machines
X Y Z
Jobs A 19 28 31
B 11 17 16
C 12 15 13
8M
Cont…2

Unit III
5. A telephone exchange has two long distant operators. The telephone company finds
that during the fashion at an average rate of 15/hr. The length mean of 5mins:
i. What is the probability that a subscriber will have to wait for his long distant dials on
the peak hour of the day
ii. What is the average waiting time for the customers
5M
Given the matrix of set-up costs, show how to sequence the production so as to
minimize the set-up cost per cycle:
To
From
A1 A2 A3 A4 A5
A1 ∞ 2 5 7 1
A2 6 ∞ 3 8 2
A3 8 7 ∞ 4 7
A4 12 4 6 ∞ 5
A5 1 3 2 8 ∞
10M
6. Explain characteristics of queuing models. 5M
In a self service store with one cashier, 8 customers arrive on an average of every
5mins. and the cashier can serve 10 in 5mins. If both arrival and service time are
exponentially distributed, then determine:
i. Average number of customer waiting in the queue
ii. Expected waiting time in the queue
iii. What is the probability of having more than 6 customers In the system
10M
Unit IV
7. State the effects of deterioration on the performance of the equipment. 3M
A fleet owner finds from his past experience records that the cost of the machine is Rs
6000/- and the running cost are given below. At what age the replacement is due:
Year 1 2 3 4 5 6 7 8
Maintenance Cost 1000 1200 1400 1800 2300 2800 3400 4000
Resale Value 3000 1500 750 375 200 200 200 200
12M
8. What are the different types of inventory? 3M
A television manufacturing company produces its own speakers, which are used in the
production of its television sets. The television sets are assembled on a continuous
production line at rate of 8,000 per month. The company is interested in determining
when and how much to procure, given the following information:
i. Each time a batch is produced, a set-up cost of Rs.12,000 is incurred
ii. The cost of keeping a speaker in stock is Rs.0.30 per month
iii. The production cost of a single speaker is Rs.0.00 and can be assumed to be a unit
cost
iv. Shortage of a speaker, (if there exists) costs Rs.1.10 per month)
12M
Unit V
9. Explain the essential features of Game Theory. 7M
Solve the following game:
Player B
Strategy B1 B2
Player A
A1 1 5
A2 4 2
8M
10. Discuss the characteristics of dynamic programming. Explain its applications. 8M
Explain the characteristics of capital budgeting. 7M