## What is degeneracy? How does the problem

## Quantitative Techniques 1

** Questions:**

**Q1.** a) “Statistics is the nerve center for Operations Research.” Discuss.

#### b) State any four areas for the application of OR techniques in Financial Management, how it improves the performance of the organization.

**Q2.** At the beginning of a month, a lady has Rs. 30,000 available in cash. She expects to receive certain revenues at the beginning of the months 1, 2, 3 and 4 and pay the bills after that, as detailed here:

**Q3.** What is degeneracy? How does the problem of degeneracy arise in a transportation problem? How can we deal with this problem?

**Q4.** Give the various sequencing models that are available for solving sequential problems. Give suitable examples.

**Q5.** A company has determined from its analysis of production and accounting data that, for a part number KC-438, the annual demand is equal to 10,000 units, the cost to purchase the item is Rs 36 per order, and the holding cost is Rs 2/unit/pear

#### a) What should the Economic Order Quantity be?

#### b) What is the optimum number of days supply per optimum order?

** Q6.** A TV repairman finds that the time spent on his jobs has an exponential distribution with a mean 30 minutes. If he repairs sets on the first-come-first-served basis and if the arrival of sets is with an average rate of 10 per 8-hour day, what is repairman’s expected idle time each day? Also obtain average number of units in the system.

**Q7.** What is critical path? State the necessary and sufficient conditions of critical path. Can a project have multiple critical paths?

**Q8.** Explain and illustrate the following principles of decision making:

#### a)Laplace

#### b) Maximin

#### c) Maximax

#### d) Hurwicz

#### e) Savage

#### f) Expectation

**Q9.** A salesman makes all sales in three cities X, Y and Z only. It is known that he visits each city on a weekly basis and never visits the same city in successive weeks. If he visits city X in a given week, then he visits city Z in next week. However, if he visits city Y or Z, he is twice as likely to visit city X than the other city. Obtain the transition probability matrix. Also determine the proportionate visits by him to each of the cities in the long run.

**Q10.** “When it becomes difficult to use an optimization technique for solving a problem, one has to resort to simulation”. Discuss.

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