Rajasthan Technical University 2010 B.Tech Mechanical Engineering Operations Research - Question Paper
Rajasthan tech. University
B.tech seven sem (Main)
January 2010
Operations Research
RoM No.
B.T*c* (S*m W) (Main) Eiamtnation, Jnu*cy 2010
gi> pouring (7Mt3 OpwWtowa Wwfch)
[Total Marks: $0 (Min. Passing Marks : 24
T*n: 3 Hours)
Attempt overall five Questions selecting one question from each unit. All questions carry equal marks. (Schematic diagrams
must be shown wherever necessary. Any data you feet
missing may suitably be assumed and stated clearly.
Units ol Quantities used/calculated must be stated clearly.)
Use of following supporting material is permitted during examination. (Mentioned in form Ato. 205)
1.___Nil__________________2.______tfil________
UNIT - I
1 (a) Discuss tli'e various phases in solving an OR problem
6
(b) Discuss t-he role of OK in decision making
(c) Construct the dual of the problem Minimize Z = * 3x>, subject to 2.t] + ,r-_ < 2 ,
x, + 2x2 + 6i3 5.
jr, + ,x2 + 2.r;l = 2 .
6
OR
1
7E4062] [I [Contd...
1 A XYZ' Company have two bottling plants, one located at u and the other at 'J'. Each plant produces three drinks A', B' and 'C'. The numbers of bottle* produced per day are as follows:
|
Drink |
Plant G |
Plant J |
|
Drink A |
I 500 |
1.500 |
|
Drink B |
i 000 |
1 000 |
|
Drink C |
2 000 |
5.000 |
The market lurvey indicated that duruig the month of April, there will b* a demand of 20.000 bottle* of dnnk A'. 40.000 bottie* of dnnk B and 44,000 bottle* of dnnk 'C' The operating costs per day of plant* at 'G' and J' are 600 and 400 monetary unit* For how many day* each piant be run in April *o a.* to minimize the production cost, while Mill meeting the market demand? Solve by two-phase Simplex method
*
UNIT - I!
2 A transport company engaged in carrying parcels* has three branches to serve five customers. The distance (km) from each branch to each of the customers is given blow :
|
Ca |
tomers |
No of trucks j | ||||
|
Bronchos |
A |
ts |
0 |
D |
E |
available 1 |
|
1 |
10 |
8 |
12 |
9 |
3 |
- 15 1 |
|
II |
4 |
4 |
G |
G |
7 | |
|
III |
15 |
7 |
11 |
r.i |
8 |
it; ' |
|
No. of trucks required |
8 |
8 |
4' |
7 |
fi |
1 |
If an arrival of a WIP blocks the traffic from branch I to customers C and D and from branch II to customers D and E, what should be the optimal allocation in order to minimize the total transportation cost ?
16
OR
2 (a) The processing times (minutes) taxm by 5 operators to make
5 different p'roducts are given below;. The effective working hours in a day are 6 :
Pr('/!ur{s * :
|
1- Operators ! ! |
2 |
3 |
4 | ||
|
A . |
10 |
12 |
18 |
15 |
9 |
|
B |
12 |
10 |
20 |
18 |
IX) |
|
V |
8 |
9 |
15 |
10 |
8 |
|
, n 1 |
9 |
8 |
24 |
12 |
12' |
|
;.....E _i |
10 |
15 |
18 |
12 |
10 |
7E4062J inilHHimil 2 [Contd...
Profits per product are Rs. 4. 2, 3. 3 and 4 for products : I. 3, 4 and 5 respectively. Find the allocation of -raters to products so as to maximize total profit.
(Jj> " plain Bellman'* principle of optimality.
UNIT - 111
3 A firm want* to determine the quantity of butterstis
pregime to meet the Jmnrt Pflnt r * 111111 F.......
following
|
Quantity Required (kg) |
N'o. of days demand occurred |
|
15 |
6 |
|
20 |
14 |
|
25 |
20 |
|
30 |
80 |
|
35 |
40 |
|
40 |
30 |
|
50 |
10 |
Ti stocks are restricted to the range of 15 to 50 kg. flue to inar r-.iuate storing facilities. Butter costs Rs. 40 per kg and is solii at Rs. 50 per kg.
(i) Construct a conditional profit table.
(ii) Determine the action alternative associated with the maximization of expected profit.
(iii) Determine EVPI.
5+6+5
OR
(a) Explain the branch and bound method in integer
programming.
(b) Solve the game whose pay-off matrix is as follows :
|
Player B | |||||||||||||||||||||||||
|
7E4062]
.(b) Derive the EOQ formal* = v2C(/?/C, . wherr the symbols '"r usual meanings.
(c) What are limitation* of tO faoula lad assumption* in EOQ formula ? s " -
OR
4 (a> What is an inventory system ? Explain clearly the different
costs that are involved in inventory problems with suitable examples.
8
(b) The annual demand for an item is 3200 units. The unit cost , * is Rs. 6 and inventory carrying charges* 25% per annum. If the cost of one procurement is Rs. 150, determine :
(i) Economic Order Quantity '
(ii) No. of orders per year
(iii) Time between two consecutive orders and
(iv) Optimal cost.
8
UNIT - V
5 (a) What do you understand by simulation ? Explain briefly the
limitations and advantages of simulation.
6
(b) Distinguish between mathematical models- and simulation models.
I
(c) Explain Monte Carlo method of simulation with suitable example.
6
OR
5 (a) Explain briefly the main characteristics of queueing system.
Describe the fundamental components of a queueing system with suitable example.
8
(b) Obtain the steady equation for the model M/M/1 : FIFO and derive the formula for
(i) average number of units in the queue
(ii) average waiting time of an arrival in the queue.
8
| 2500 1
|
Attachment: |
| Earning: Approval pending. |
