a$.$ What will be the proceeds and nel profits to an investor who purchases the Ociober $2011$ expiration IBM calls with exercise price S$165$ it the stock price al oplion expiralion is S$155?$ What if the stock price at expiration is $$175?$

b$.$ Now answer part $($a$)$ for an irvestor who purchases the October expiration IBM put opion with exercise price $$165.$