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You have shorted a put option on Ford stock with a strike price of $$8.$ When you sold $($wrote$)$ the put, you received $$3.$ The option will expire in exactly six months' time.

a$.$ If the stock is trading at $$5$ in six months, what will your payoff be$?$ What will your profit be$?$

b$.$ If the stock is trading at $$17$ in six months, what will your payoff be$?$ What will your profit be$?$

c$.$ Draw a payoff diagram showing the value of the put at expiration as a function of the stock price at expiration.

d$.$ Redo c$,$ but instead of showing payoffs, show profits.

a$.$ The payoff of the short is $ $($Round to the nearest dollar.$),$ and the profit of the short is $