Section A (20 Marks)
Write short notes on any four of the following:
1. Managerial Decision Making Environment
2. The Bernoulli Process
3. Duality Theorem
4. Steps in Decision Theory
5. Use of Matrices for Production Planning
Section B (30 marks)
(Attempt any three)

Define functions. What are the different types of functions?
2. Find two consecutive numbers such that 5 times the smaller number is equal to 5 more than three times the greater number.
3. Distinguish between objective probability and subjective probability. Give one example of each concept.
4. What are the different types of transportation problems?
Section C (50 marks)
(Attempt all questions. Every question carries 10 marks)
Read the case “Selecting Distribution Type” and answer the following questions:
Case Study: Selecting Distribution Type
In each of the following three situations, use the binomial, Poisson or normal distribution according to which it is most appropriate. In each case, explain why you selected the distribution and draw attention to any feature which supports or casts doubt on the choice of distribution.
Situation 1
The lifetimes of a certain type of electrical component are distributed with a mean of 800 hours and a standard deviation of 160 hours.
Questions
1. If the manufacturer replaces all components that fall before the guaranteed minimum lifetime of 600 hours, what percentage of the components has to be replaced?
2. If the manufacturer wishes to replace only the 1% of components that have the shortest life, what value should be used as the guaranteed lifetime?
3. What is the probability that the mean lifetime of a sample of 25 of these electrical components exceeds 850 hours?
Situation 2
A green grocer buys peaches in large consignments directly from a wholesaler. In view of the perishable nature of the commodity, the green grocer accepts that 15% of the supplied peaches will usually be unsaleable. As he cannot check all the peaches individually, he selects a single batch of 10 peaches on which to base his decision of whether to purchase a large consignment or not. If no more than two of these peaches are unsatisfactory, the greengrocer purchases the consignment.
Question
4. Determine the probability that, under normal supply conditions, the consignment is purchased.
Situation 3
Vehicles pass a certain point on a busy singlecarriageway road at an average rate of two per tensecond interval.
Question
5. Determine the probability that more than three cars pass this point during a twentysecond interval.