Consider a perpetual American put option with K = $50, 4 = 30%, and r = 1%. Suppose that today the price of the stock is $50, what is the optimal exercise boundary b? Suppose that today the price of the stock is $60, what is the optimal exercise boundary b? Pick any number between the value of b you found earlier and K. If the stock price is equal to that value today, what is the optimal exercise boundary b?