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 $K100,000.$ The manager of research programme said

that there is $60\%$ 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 $K100,000.$ The present value of profit for the second proposal was $K120,000.$

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 $K100,000?$

$(2$ 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 $75$ persons arrive in an $8$

$-$hour day. Each tax adviser spends $25$ 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: $20$ MARKS$]$