A new model for a full$-$service gas station has been developed and offers a deluxe service

for customers coming in for a fill$-$up of gasoline. Four workers approach the car at the

same time and begin the service. Worker #$1$ asks the customer what kind of gasoline

he$/$she would like $(10$ seconds$)$ and then pumps the gas into the car $(72$ seconds$).$ Worker

#$2$ checks the oil level in the car $(24$ seconds$)$ and then fills all fluids that are low $(40$

seconds$).$ Worker #$3$ checks the air pressure in the tires $(57$ seconds$)$ and the fills up the

tires that are low $(65$ seconds$).$ Worker #$4$ washes all of the windows of the vehicle $(82$

seconds$).$ When all work activities are completed, Worker #$4$ approaches the customer

and tells them the total cost of the service $(12$ seconds$)$ and then processes the payment

$(63$ seconds$).$

a$.$ Develop a deterministic PERT Chart for this system and identify the critical path.

b$.$ What is the allowable delay in the time for Worker #$2$ to perform his second work

activity?

c$.$ What is the allowable delay in the time for Worker #$3$ to complete her first work activity?

d$.$ A review of this system reveals that representing this system deterministically is a gross

over$-$simplification and it is suggested that the PERT $3$ estimate technique be employed

to evaluate the system probabilistically. Analysis reveals the following data.

i$.$ A customer arrives and asks "What is the probability that the team could finish

my car in $190$ seconds?" What is your reply?

ii$.$ Another customer arrives and asks "What is the probability that my car will not be

ready in $210$ seconds?" What is your reply?

iii. Another customer arrives and asks "What is the probability that my car will be

completed in time frame of $180-195$ seconds?" What is your reply?