The Newcoat Painting Company has for some time been experiencing high demand for

Question

The Newcoat Painting Company has for some time been
experiencing high demand for its automobile repainting
service. Since it has had to turn away business, management
is concerned that the limited space available to store cars
awaiting painting has cost lost revenue. A small vacant lot
next to the painting facility has recently been made available
for lease on a long-term basis at a cost of $10 per day.
Management believes that each lost customer costs $20 in
profit. Current demand is estimated to be 21 cars per day
with exponential interarrival times (including those turned
away), and the facility can service at an exponential rate of
24 cars per day. Cars are processed on an FCFS basis.
Waiting space is now limited to 9 cars but can be increased
to 20 cars with the lease of the vacant lot. Newcoat wants
to determine whether the vacant lot should be leased.
Management also wants to know the expected daily lost
profit due to turning away customers if the lot is leased.
Only one car can be painted at a time.

Explanation / Answer

imagine for one year :

10 / day for one year accounts to 3650 $

i think the land should be leased for better business.

if the lot is leased :

waiting space is now 11 greater than the previous 9.

so, 1 gives 20 $ in profit

11 gives 220 $ in profit.

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