You have shorted a put option on Ford stock with a strike price of $$15.$ When you sold $($wrote$)$ the put, you received $$7.$ The option will expire in exactly

six months' time.

a$.$ If the stock is trading at $$8$ in six months, what will your payoff be$?$ What will your profit be$?$

b$.$ If the stock is trading at $$26$ 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 $$,$ and the profit of the short is $$.$

$($Round to the nearest dollar.$)$