Decision Tree Model Question:

Assume a car rental dealership has a rental rate of $300 per day. Currently, daily demand is approximately normally distributed with a mean of 7 cars per day, and a Standard Deviation of 3.

The dealership wants to know if they're leaving money on the table and could potentially rent out more cars each day. However, each extra car

will cost the car rental dealership $45/day in leasing costs, $10/day in insurance and $5/day for cleaning and maintenance.

Additionally, they have estimated the loss of goodwill for turning away an additional customer at $150.

a) How many cars should the rental company have in their fleet? Show with a decision tree and calculate using expected value. Please ignore the loss of goodwill for this question.

b)How many cars should the rental company have in their fleet if we incorporate the loss of goodwill. Has the fleet size increased or decreased as compared to the scenario in part a? Does this make intuitive sense? Why or why not?