You currently hold $200$ shares worth $3,200$ of company Dunder Mifflin on $1$ May $2023.$ To protect yourself from potential stock price drop, you bought an August put option for $2,000$ shares with an exercise price of $15.$ The option costs you $200.$

Requirements

a$)$ What is your total profit if the share price becomes $20$ in August? $(4$ marks$)$

b$)$ What is your total profit if the share price becomes $12$ in August? $(4$ marks$)$

c$)$ What is the price in August that will generate the same profit for you with and without buying the put option? $(4$ marks$)$