Madras University (UnOM) 2006 M.C.A Computer Aplications Operations Research - Question Paper

Time: 3 hours
Maximum: 75 marks

Use of statistical table is permitted.

PART A - [5 x five = Marks 25]

ans ALL ques..
every ques. carries five marks.

1. (a) The manager of an oil refinery must decide on the optimum mix of two possible blending processes of which the inputs and outputs production run are as follows:
Input Output

Process Crude A Crude B Gasoline X Gasoline Y

1 6 4 6 9
2 5 6 5 5
The maximum amounts available of crudes A and B are 250 units and 200 units respectively. Market demand indicates that atleast 150 units of gasoline X and 130 units of gasoline Y must be produced. The profits per production run from Process one and Process two are Rs. four and Rs. five respectively. Formulate the issue for maximising the profit.

(b) Solve graphically the subsequent L.P.P.:
Maximise z = 3x1 + 2x2
Subject to the constraints
-2x1 +x2 <= 1
x1 < = 2
x1+x2 < = three and
X1 , x2 = > 0.

2. (a) Use Vogel's approximation method to find an initial basic feasible solution of the transportation problem:

D E F G Available

A 11 13 17 14 250

B 16 18 14 10 300

C 21 24 13 10 400

Demand 200 225 275 250
Or

(b) Write short note on the travelling-salesman issue.

3. (a) Sketch the Branch and Bound Method in integer programming.

Or

(b) Use dynamic programming to solve the subsequent L.P.P. :
Maximize z = 3x1 + 5X2
Subject to the constraints
x1 < = 4, X2< =6 6,
3x1 + 2X2 <= 18 and
X11 X2 => 0

4. (a) A book binder has 1 printing press, 1 binding machine, and the manuscripts of a number of various books. The time needed to perform the printing and binding operations for every book are shown beneath. Determine the order in which book should be processed, in order to minimize the total time needed to turn out all the books:

Book one two three four five 6
Printing time (hrs.): 30 120 50 20 90 110
Binding time (hrs.): 80 100 90 60 3010

Or

(b) discuss the subsequent terms:
(i) Free and Total Float.
(ii) Critical path.
(iii) Pessimistic, optimistic and most likely times.

5. (a) Let X(t) = A cos at + B sin a where A, B are uncorrelated random variables every with mean 0 and variance one and w is a positive constant. Is {X(t)} covariance stationary?

Or

(b) What do you understand by
(i) queue length.
(ii) traffic intensity.
(iii) steady and transient state.
(iv) Balking.
(v) Queue discipline.

PART B - [5 x 10 = Marks 50]
ans any 5 ques..
every ques. carries 10 marks.

6. Solve the subsequent issue by simplex method:
Maximise z = 107x1 + X2 + 2X3
Subject to the constraints
14x1 + X2 - 6X3 + 3X4 7
16x1 + x2 - 6X3 five 2
3x1 - X2 - X3 0
X1 I X2, X3 ,X4 0 .

7. Use dual simplex method to solve the subsequent L.P.P. :

Maximize z = -3x1 - X2


Subject to the constraints

X1 + X2 => 1
2x1 + 3X2 >2
X1 one X2 =0.

8. A department head has 4 tasks to be performed and 3 subordinates, the subordinates differ in efficiency. The estimates of the time, every subordinate would take to perform, is provided beneath in the matrix. How should he allocate the tasks 1 to every man, so as to minimize the total man-hours?
Men

Task 1 2 3

1 9 26 15

11 13 27 6

111 35 20 15

IV 18 30 20
9. Solve the subsequent issue using Gomary's cutting plane method:
Maximize Z = X1 + X2
Subject to the constraints
3x1 + 2X2 < = 5
X2 < = 2
X1 I X2 => 0 and x1 is an integer.

10. obtain an optimal sequence for processing the nine jobs through the machines A, B, C in the order ABC. Processing times are provided beneath in hours. obtain the total elapsed time for the optimal sequences.

Jobs one two three four five six seven eight 9
Machine A four nine five 10 six 12 eight three 8
Machine B six four eight nine four six two six 4
Machine C 10 12 nine 11 14 15 10 14 12

11. Assuming that the expected times are normally distributed, obtain the probability of meeting the schedule date as provided for the network.
Activity (I - j) : 1-2 1-3 2-4 3-4 4-5 3-5
Optimistic (days): 2 9 5 2 6 8
Most likely 5 12 14 5 6 17
Pessimistic 14 15 17 12 12 20
Scheduled Project completion date is 30 days. Also obtain the date on which the project manager can complete the project with a probability of 0.90.

12. A car park contains five cars. The arrival of cars is Poisson at a mean rate of 10 per hour. The length of time every can spends in the car park is exponential distribution with mean of five hours. How many cars are in the car park on an average?

13. A barber shop has 2 barbers and 3 chairs for customers. presume that the customers arrive in Poisson fashion at a rate of five per hour and that every barber services customers according to an exponential distribution with mean 15 minutes. Further, if a customer arrives and there are no empty chairs in the shop, he will leave. What is the expected number of customers in the shop?

Earning:   Approval pending.