Consider a one-step binomial model for a stock. Now, the stock is worth S0, but will be worth either S0u or S0d at time T where d<1

a) Consider an American put on the stock with strike price K where K > S0u. Show that it is always better to exercise the put early when r > 0.

b) Consider an American put with strike price K where K < S0d. What is the value of the put now?

c) Find the number? Such that when the strike price K is bigger than, it is better to exercise the option early and when the strike price is less than, it is better to wait until expiration.