Total No. of Questions 10] [Total No. of Pages 04
M.Sc. DEGREE EXAMINATION, MAY 2017
Second Year
STATISTICS
Operations Research
Time 3 Hours Maximum Marks: 70
Answer any FIVE questions
All questions carry equal marks
Q1) Use simplex method to solve the following L.P.P:
Maximize Z 3x1 2x2 3x3
Subject to the constraints 2x1 x2 x3 2
3x1 4x2 2x3 8
and x1, x2 x3 0.
Use duality to solve the following L.P.P:
Maximize Z 2x1 x2
Subject to the constraints: x1 2x2 10
x1 x2 6
x1 − x2 2
x1 − 2x2 1
and x1, x2 0.
Q2) Use dual simplex method to solve the following L.P.P:
Minimize Z 6x1 x2
Subject to the constraints 2x1 x2 3
x1 − x2 0
and x1, x2 0.
Use two-phase simplex method to solve the following L.P.P:
Minimize Z x1 2x2
Subject to the constraints: 2x1 5x2 6
x1 x2 2
and x1, x2 0.
Q3) What are inventory models? Discuss EOQ model with different rates of
demand.
A firm has a machine whose purchase price is Rs. 1,00,000. Its running cost
and resale price at the end of different years are as follows:
Year 1 2 3 4 5 6
Running cost 7,500 8,500 10,000 12,500 17,500 27,500
Resale price 85,000 76,500 70,000 60,000 40,000 15,000
The firm has obtained a contract to supply the goods produced by the
machine, for a period of 5 years from now. After this time period the firm
does not intend to use the machine. If the firm has a machine of this type,
that is one year old, what replacement policy should it adopt if it intends to
replace the machine not more than once?
Q4) Explain the policies for replacement of items that fail completely.
An item is produced at the rate of 50 items per day. The demand occurs at
the rate of 25 items per day. If the set-up cost is Rs. 100 per set-up and the
holding cost is Re. 0.01 unit of item per day, find the economic lot size for
one unit, assuming that shortage is not permitted. Also find the time of
cycle and minimum total cost for one run.
Q7) Explain queuing system. Obtain its steady state solution. Find the waiting time distribution for the system.
Explain queuing system. Obtain Pollaczee Kinchine formula.
Q8) Explain queuing system. Obtain its steady state solution. Find the
average number of customers in the system.
Explain M/Ek/1 system. Obtain its steady state solution. Obtain the
average waiting time of the phases in the system.
Q9) Explain the significance of using PERT/CPM. Describe the rules for
activity-on-arrow network construction.
A socliologist plans a questionnaire survey consists of the following
details:
Duration (days)
Activity Immediate Likely Minimum Maximum
Predecessor
A 5 4 6
B 12 8 16
C A 5 4 12
D B 3 1 5
E A 2 2 2
F B 5 4 6
G F 14 10 18
H G 20 18 34
Draw the network diagram. Find the critical path. What is the probability
that the length of the critical path does not exceed 60 days?
Q10) Describe the phases of project management. Explain different types of
floats and their use.
Consider a project having the following details:
Activity time (weeks).
Activity Immediate
Predecessor Likely Minimum Maximum
A 3 1 5
B 4 2 6
C A 5 3 7
D A 6 5 7
E C 7 5 9
F D 8 6 10
G B 9 7 11
H G 3 2 4
Draw the network. Find the critical path. What project duration will have
99% confidence of completion.