BA 9226 APPLIED OPERATIONS RESEARCH FOR MANAGEMENT(Regulation
2009)
Time : Three hours Maximum : 100 MarksAnswer ALL questions
PART A (10 2 = 20 Marks)1. List the scope of applications of OR
techniques.2. What is sensitivity analysis?3. List the methods used
to arrive at an initial basic feasible solution in atransportation
model.4. How does a travelling salesman problem differ from a
routine assignmentmodel?5. Define zero sum game.6. What is a mixed
integer programming problem?7. Define simulation.8. What is meant
by EOL?9. What is the significance of r in a replacement model?10.
List the applications of queuing models.PART B (5 16 = 80 Marks)11.
(a) A person requires 10, 12, and 12 units of a dry and liquid
combination ofchemicals A, B and C respectively for his garden. A
liquid productcontains 5, 2 and 1 units of A, B and C respectively
per jar. A dry productcontains 1, 2 and 4 units of A, B and C per
carton. If the liquid productsells for Rs. 3 per jar and the dry
product sells for Rs. 2 per carton, howmany of each should he
purchase in order to minimize the cost and meetthe requirement?
(16)Or(b) Maximise z = z y x 3 2 5 + Subject to:0 , ,5 33 4 32 2
2>=
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z y x(16)12. (a) Find the minimum cost distribution plan to
satisfy demand for cement atthree construction sites from available
capacities at the three cementplants given the following
transportation costs (in Rs) per ton of cementmoved from plants to
sites.From To construction sites Capacity (tons / month)1 2 3P1 300
360 425 600P2 390 340 310 300P3 255 295 275 1000Demand (tons/month)
400 500 800Or(b) A company is faced with the problem of assigning 4
machines to6 different jobs (one machine to one job only). The
profits are estimatedas follows. Solve the problem to maximize the
total profits.Job MachineA B C D1 3 6 2 62 7 1 4 43 3 8 5 84 6 4 3
75 5 2 4 36 5 7 6 413. (a) Solve Max z = y x 4 +subject to : 2x +
4y < = 7, 5x + 3y < = 15, where x and y are
positiveintegers.Or132 132 132
96515 3(b) Solve the following game whose payoff matrix is given
below.Player BPlayerAB1 B2 B3 B4A1 5 10 9 0A2 6 7 8 1A3 8 7 15 2A4
3 4 -1 414. (a) The annual demand for a product is 100000 units.
The rate of productionis 200000 units per year. The set-up cost per
production run is Rs. 5000and the variable production cost of each
item is Rs 10. The annual
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holding cost per unit is 20% of its value. Find the optimum
production lot size and the length of the production run.Or(b) A
manager has a choice between(i) A risky contract promising Rs 7
lakhs with probability 0.6 andRs. 4 lakhs with probability 0.4
and(ii) A diversified portfolio consisting of two contracts with
independentoutcomes each promising Rs 3.5 lakhs with probability
0.6 andRs. 2 lakhs with probability 0.4. Using the EMV criteria
suggest acontract.15. (a) There are two clerks in a university to
receive fees from the students. Ifthe service time for each student
is exponential with mean 4 minutes andif the boys arrive in a
Poisson fashion at the counter at the rate of 10 perhour,
determine(i) The probability of having to wait for service (8)(ii)
The expected percentage idle time for each clerk. (8)Or(b) The
probability Pn of failure just before age n is shown below for1000
bulbs. If the individual replacement costs Rs. 1 and the
groupreplacement costs Rs. 0.3 per item, find the optimal
replacement policy.n : 1 2 3 4 5Pn : 0.3 0.1 0.1 0.2 0.3
