Jawaharlal Nehru Technological University Hyderabad 2010-2nd Sem M.C.A -ester Supplementary s OPERATIONS RESEARCH - Question Paper

Code No: 32004
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
MCA-II Semester Supplementary exams July 2010
OPERATIONS RESEARCH
Time: 3hours Max.Marks:60
ans any 5 ques.
All ques. carry equal Marks
- - -
1.a) explain the scope of OR in various fields.
b) 3 grades of coal A, B and C contain phosphorus and ash as impurities. In a
particular industrial process, fuel upto 100 tons (max) is needed which should
contain ash not more than 3%. It is desired to maximize the project while satisfying
these conditions. There is an unlimited supply of every grade. The percentage of
impurities and the profits of grades are provided beneath.
Coal Phosphorus (%) Ash (%) Profit in Rs. per ton
A 0.02 2.0 12.00
B 0.04 3.0 15.00
C 0.03 5.0 14.00
obtain the proportion in which the 3 grades be used.
2. Consider the issue of assigning 5 jobs to men. The costs are provided in the table
below. Determine the optimum assignment schedule.
1 two three four 5
A eight four two six 1
B 0 nine five 5 4
C three eight nine two 6
D four three one 0 3
E nine five eight nine 5
3. A salesman wants to visit A, B, C, D & E. He does not want to visit any city twice
before completing his tour. obtain the lowest cost route.
A B C D E
A - two five seven 1
B six - three eight 2
C eight seven - four 7
D 12 four six - 5
E one three two eight -
4. In a machine shop, a particular cutting tool costs Rs six to change. If a tool breaks on a
job the production disruption & associate costs amount to Rs 30. The past life of a
tool is provided as follows.
After how many jobs should the shop change a tool before it breaks down?

Job No one two three four five six 7
Proportion on broken
tools on job
0.01 0.03 0.09 0.13 0.25 0.55 0.95

5. Consider a self service store with 1 cashier. presume Poisson arrivals and
exponential service times. Suppose that 9 customers arrive on the avg. every 5
minutes and the cashier can serve 10 in five minutes, obtain
i) The avg. no. of customers queuing for service
ii) The probability of having more than 10 customers in the system,
iii) The probability that a customer has to queue for more than two minutes.
6. A manufacturing company requires 15000 units of a part annually for an assembly
operation. The manufacturer can produce this part at the rate of 100 units per day and
the set up cost for every operation run is Rs 24. To hold 1 unit of his part in
inventory costs the manufacturing Rs.5 per year. Assuming 250 working days per
year, what will be the optimum manufacturing quantity? Prove the formula used. obtain
optimum length of time ranging from orders. What will be the inventory management
cost/year and total cost per year? 1 unit cost Rs 7/- only.
7.a) What is strictly determined game?
b) Solve the subsequent game whose payoff matrix is provided beneath.
Player A
Player B -34 -17 --24 --52 --61
8. Solve the subsequent LPP using dynamic program approach.
Max Z = 3x1 + 5x2. St
1
2
1 2
1 2
4
6
3 two 18
, 0
x
x
x x
x x
=
=
+ =
=

Earning:   Approval pending.