QUESTIONFOUR

A project has the following characteristics:

$($a$)$ Construct the network

$($b$)$ Find the critical path and variance for each event

$($c$)$ Find the project duration at $95\%$ probability.QUESTION FIVE

$($a$)$ A self $-$ service store employs one cashier at its counter. Nine customers arrive on an

average every $5$ minutes while the cashier can serve $10$ customers in $5$ minutes. Assuming

Poisson distribution for arrival rate and exponential distribution for service time, find

i$.$ Average number of customers in the system

ii$.$ Average number of customers in the queue or average queue length

iii. Average time a customer spends in the system

iv$.$ Average time a customer waits before being served

$($b$)$ A tax consulting firm has $3$ counters in its office to receive people who have problems

concerning their income, wealth and sales taxes. On the average $48$ persons arrive in an $8$

$-$hour day. Each tax adviser spends $15$ 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

ii$.$ The average number of customers in the system

iii. Average number of customers waiting to be served

iv$.$ Average time a customer spends in the system

v$.$ Average waiting time for a customer