1. 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 itimproves the performance of the organization.
2. 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:
| Month | Revenue | Bills |
| 1 | Rs. 28,000 | Rs. 36,000 |
| 2 | Rs. 52,000 | Rs. 31,000 |
| 3 | Rs. 24,000 | Rs. 40,000 |
| 4 | Rs. 22,000 | Rs. 20,000 |
It is given that any money left over may be invested for one month at the interest rate of 0.5%; for twomonths at 1.0% per month; for three months at 1.5% per month and for four months at 1.8% per month.
Formulate her problem as linear programming problem to determine an investment strategy that maximizes cash in hand at the beginning of month 5.
3. What is degeneracy? How does the problem of degeneracy arise in a transportation problem? How can we deal with this problem?
4. Give the various sequencing models that are available for solving sequential problems. Give suitable examples.
5. A company has determined from its analysis of production and accounting data that, for a part numberKC-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
Determine:
a. What should the Economic Order Quantity be?
b. What is the optimum number of days supply per optimum order?
6. 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.
7. What is critical path? State the necessary and sufficient conditions of critical path. Can a project havemultiple critical paths?
8. Explain and illustrate the following principles of decision making:
a. Laplace
b. Maximin
c. Maximax
d. Hurwicz
e. Savage
f. Expectation
9. 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.
10. When it becomes difficult to use an optimization technique for solving a problem, one has to resort to simulation‖. Discuss.