$2.$Suppose that you long a put option contract with a strike price of $$65$ that costs $$3$ and expires in $3$ months. The stock is currently trading at $$59,$ and the size of the contract is $100$ shares.a$)$Do you gain or lose at $$59?$ Show your calculationsb$)$At what range of stock prices would you gain?c$)$At what range of stock prices would you lose?d$)$At what range of stock prices should you exercise the option?e$)$At what range of stock prices you should not exercise the option?f$)$Draw a diagram illustrating how the profit from a long position in this put option depends on the stock price.