Madurai Kamraj University (MKU) 2006 M.Sc Mathematics "OPERATIONS RESEARCH" - Question Paper
This Is for the MK DDU - "MSC Maths In in MKU", and please Refer to the Attached File,
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It's For "Msc in MATHS in MKU", It'a Course in "Madurai Kamaraj University" or %MK University%
The paper Name Is "OPERATIONS RESEARCH"
(6 pages) (
Paper VI OPERATIONS RESEARCH
3. For the network given below, find the minimum time of completion of the project. Also identify the critical path.
Use dynamic programming to find the value of Minimize z - yl + y\ + y\
Subject to
Solve the following 2x5 game by graphic mehtod.
Playe B
r
Player A
-5 5
0-18
8-4-1
V.
6 5 J
6. Explain the Branch and Bound method.
7. A branch of National Bank has only one typist. Since the typing work varies in length (number of pages to be typed), the typing rate is randomly distributed approximating a Poisson distribution with mean service rate of 8 letters per hour. The letter arrive at a rate of 5 per hour during the entire 8-hour work day. If the typewriter is valued at Rs. 1.50 per hour, determine
(a) Average system time
(b) Average idle time cost of the typewriter per
day.
8. Find the minimum of the function
f Oe) = xf + x2 + x% - 4x1 - 8*2 - 12x3 +56. SECTION B (3 x 20 = 60 marks)
Answer any THREE questions.
9. (a) Describe the role of duality for sensitivity analysis of an L.P. problem.
(b) Consider the problem
Maximize z =5x1 + Zx2 + 7xs Subject to
+ x2 + x3 < 22 3*! + 2x2 +*3 26 x! + x2 + *3 < 18
J-l> X2, 3 U.
it will be the solution if the first constraint iges to x1 + x2 + 2xa <26?
10. Solvit the following integer programming problem
\
Maximize z = 2*! + &c2 Subject to
6*! + 5x2 < 25 + 3x2 10 xv x2 0
and integers.
11. 'A project is represented by the network given below. The activity times are given below.
Activity: ABCDEFGHI
Optimistic time: 5 18 26 16 15 6 7 7 3
Most likely time: 8 20 33 18 20 9 10 8 4
Pessimistic time: 10 22 40 20 25 12 12 9 5
Determine the following:
(a) Expected task times and their variances
(b) The critical path
(c) The probability of completing the project in 41.5 weeks.
fP.T.O.l
12. (a) . Explain the Birth-Death process.
(b) A shipping company has a single unloading dock with ships arriving in a Poisson fashion at an average rate of 3 per day. The unloading time distribution for a ship with n unloading crews is found
to be exponential with average unloading time days.
2 n
The company has a large labour supply without regular working hours and to avoid long waiting times, the company has a policy of using as many unloading crews as there are ships waiting in line or being unloaded. Find
(i) the average number of unloading crews working at any time and
(ii) the probability that more than 4 crews will be needed.
13. Apply Wolfes method to solve the quadratic programming problem :
Maximize z = 2xx + x2 - xj2 Subject to
2x1 + 3jc2 < 6 2xx +. x2 < 4 Xj, x2 0.
14. Use separable programming algorithm to the nonlinear programming problem:
Maximize z = + x\
Subject to the constraints :
3*! + 2x% < 9 > 0, x2 > 0.
6 6561/KA6
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