Tim Waltzer owns and operates Waltzer€™s Wrecks, a discount car rental agency near Cleveland Hopkins International Airport. He rents a wreck for $20 a day. He has an arrangement with Landrum Leasing to purchase used cars at $6,000 each. His cars receive only needed maintenance and, as a result, are worth only $2,000 at the end of the year of operation. Tim has decided to sell all his wrecks every year and purchase a complete set of wrecks from Landrum Leasing. His clerk-accountant provided him with a probability distribution with respect to the number of cars rented per day.

Tim is an avid golfer and tennis player. He is either on the golf course on weekends or playing tennis indoors. Thus, his car rental agency is only open weekdays. Also, he closes for 2 weeks during the summer and goes on a golfing tour.
The clerk-accountant estimated that it cost $1.50 per car rental for minimal maintenance and cleaning.
a. How many cars should he purchase to maximize profit?
b. What is the expected value of perfect information?

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Numbers of Cars Rented per Day 21 22 23 20 20 Probablity .50 .20 .10