Firstranker's choice
Code No: 812AK
--- Content provided by FirstRanker.com ---
R13
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
MCA I Semester Examinations, October / November - 2020
OPERATIONS RESEARCH
Time: 2 Hours Max. Marks: 60
--- Content provided by FirstRanker.com ---
Answer any five questions
All questions carry equal marks
3.a) Solve the following LPP problem by two-phase method
Max Z = 2x1 + 3x2 + 5x3, Subject to
3x1 + 10x2 + 5x3 = 15
--- Content provided by FirstRanker.com ---
3x1 - 10x2 + 9x3 = 33
x1 + 2x2 + 3x3 = 4, x1, x2, x3 = 0 [12]
b) Solve the following transportation problem with initial basic feasible solution by North-West corner method. Find the optimal solution. [12]
| S1 | S2 | S3 | S4 | Supply | |
|---|---|---|---|---|---|
| Factory A | 7 | 10 | 12 | 10 | 40 |
| Factory B | 9 | 12 | 10 | 10 | 30 |
| Factory C | 12 | 9 | 14 | 12 | 20 |
| Requirement | 25 | 15 | 30 | 10 |
State the traveling salesman problem.
Solve the following traveling salesman problem
--- Content provided by FirstRanker.com ---
c12=4, c13=7, c23=6, c24=3 and c34=7 Where cji=cij [12]
Six jobs are to be processed on three machines A, B, C with the order of processing jobs as CBA
| Job | U | V | W | X | Y | Z |
|---|---|---|---|---|---|---|
| Proc. time on machine A | 12 | 10 | 9 | 14 | 7 | 9 |
| Proc. time on machine B | 7 | 6 | 6 | 5 | 4 | 4 |
| Proc. time on machine C | 6 | 5 | 6 | 4 | 2 | 4 |
The suggested sequence is Y-W-Z-V-U-X. Find out the elapsed time for the sequence suggested. Is it optimal? If it is not optimal, then find out the optimal sequence and the minimum total elapsed time associated with it. Also find the idle time on each machine. [12]
Assume that present value of one rupee to be spent in a year’s time is Rs.0.90 and C=Rs.3000 capital equipment and the running costs are given in the table below.
| Year | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| Running cost (Rs.) | 500 | 600 | 800 | 1000 | 1300 | 1600 | 2000 |
When should the machine be replaced? [12]
--- Content provided by FirstRanker.com ---
6. Find the shortest route from city A to city J along arcs joining various cities lying between A & J. Distances between cities are given as follows: [12]
| B | C | D | |
|---|---|---|---|
| A | 2 | 4 | 3 |
| E | F | G | |
|---|---|---|---|
| B | 7 | 4 | 6 |
| C | 3 | 2 | 4 |
| D | 4 | 1 | 5 |
| J | |
|---|---|
| E | 6 |
| H | |
|---|---|
| F | 3 |
| I | |
|---|---|
| G | 4 |
7. If a product is to be manufactured within the company, the details are as follows:
Annual demand rate, r=36000 units
Production rate, k=72000 units
--- Content provided by FirstRanker.com ---
Setup cost, Co=Rs. 250 per setup
Carrying cost, Ci= Rs.25/unit/year.
Find the a) EOQ and b) Cycle time. Derive relevant expressions and use. [12]
8. In a railway yard goods train arrive at a rate of 30 trains/day. Assuming that the inter-arrival time follows an exponential distribution and service time distribution is also exponential with an average 36 minutes: Calculate the following:
a) The average number of trains in the queue.
--- Content provided by FirstRanker.com ---
b) The average waiting of a train in the system.
c) The probability that the number of trains in the system exceeds 10. [12]
---00000---
--- Content provided by FirstRanker.com ---
This download link is referred from the post: JNTUH MCA 2nd Sem Last 10 Years 2023-2013 Question Papers R20-R09 || Jawaharlal nehru technological university