QUESTION ONE

$($

a

$)$

$$Mr

$.$

$$Sakala is interested in developing and marketing a new drug. The cost of extensive

research to develop the drug would be

$$

$1$

$0$

$0$

$,$

$0$

$0$

$0$

$.$

$$The manager of research programme said

that there is

$6$

$0$

$\%$

$$chance that the drug will be developed successfully. The market potential

is assessed as follows with present value of profit:

The present value figures do not include the cost of research. While Mr

$.$

$$Sakala was

considering this proposal, another similar proposal came up which also required the

investment of

$$

$1$

$0$

$0$

$,$

$0$

$0$

$0$

$.$

$$The present value of profit for the second proposal was

$$

$1$

$2$

$0$

$,$

$0$

$0$

$0$

$.$

The return on the investment in the second proposal is almost certain.

i

$.$

$$Draw a decision tree for Mr

$.$

$$Sakala indicating all choices and events

$($

$4$

$$marks

$)$

ii

$.$

$$What decision Mr

$.$

$$Sakala should take regarding the investment of

$$

$1$

$0$

$0$

$,$

$0$

$0$

$0$

$?$

$($

$2$

$$marks

$)$

iii. If Mr

$.$

$$Sakala is a risk averter, should he change the decision given by you?

$($

$2$

$$marks

$)$

$($

b

$)$

$$A tax consulting firm has

$5$

$$counters in its office to receive people who have problems

conceming their income, wealth and sales taxes. On the average

$7$

$5$

$$persons arrive in an

$8$

$-$

hour day. Each tax adviser spends

$2$

$5$

$$minutes on an average on an arrival. If the arrivals

are Poissonly distributed and service times are according to exponential distribution, find

i

$.$

$$The probability of there being no customer in the system

$($

$4$

$$Marks

$)$

ii

$.$

$$The average number of customers in the system

$($

$3$

$$Marks

$)$

iii. Average number of customers waiting to be served

$($

$2$

$$Marks

$)$

iv

$.$

$$Average time a customer spends in the system

$($

$2$

$$Marks

$)$

v

$.$

$$Average waiting time for a customer

$($

$1$

$$Marks

$)$

$[$

TOTAL:

$2$

$0$

$$MARKS

$]$

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