### Experiencing high demand for automobile repainting service

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Review Problem #8 Chapter 20 Operations Research by Wayne Winston

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.

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