$(16$ points$)$ Special Agent Dale Cooper is evaluating option strategies that will allow him to profit from large moves in a stock's price, either up or down. He believes that a combination of $2$ long put options and $1$ long call option with the same expiration and exercise price would be his objective. TWPK stock is currently trading at $$30$ per share. A six month call option on TWPK stock with an exercise price of $$30$ is currently trading at $$6.$ The semi$-$annual $($six$-$month$)$ risk free rate of interest is $2\%.$

a$.$ What is the price of one six month put option on TWPK stock with an exercise price of $$30?$

b$.$ In the space below, draw the payoff and the profit to this strategy on the same graph. Label the payoff line, the profit line, the axes, the exercise price $($with a dollar amount$),$ and the point where the payoff intersects the vertical axis $($with a dollar amount$).$

c$.$ Calculate the dollar amounts of the following in the space below and label on the above graph:

i$.$ Maximum loss

ii$.$ Breakeven stock price$($s$)$ of the position