1. A discount car rental business rents out cars for K20 a day and has an arrangement with a leasing company to purchase used cars at K6 000 each. The cars receive only needed maintenance and as a result are worth only K2 000 at the end of the first year of operation after which they are all sold and new ones bought.

Average number of cars rented per day

20 21 22 23

Probability .10 .20 .50 .20

It costs the car rental business K1.50 per car rental for minimal maintenance and cleaning.

a. How many cars should he purchase every year to maximise profits?

b. What is the expected value of perfect information?