You are attempting to formulate an investment strategy. In particular, youshorta put option with strike price X₁equals to $95 and youlonganother put option with strike price X₂equals to $115. Both put options have the same underlying stock and will expire at time T.

(a) Plot the payoff structure of this investment strategy as a function of S_T,which stands for the price of the underlying stock at maturity. The X-axis for S_tand the Y-axis is the total payoff. [hint: you can first calculate the total payoff in the three scenarios: S_T< 100, 100S_T115 and S_T> 115.]\

(b) given the following information:

Stock price right now S₀= $100, X₁= $95, X₂= $115; the annualised risk free rate at 2%; volatility of the stock = 0.18; T equals to 5 years. The stock has a policy of not paying out any dividends. BAsed on these information, calculate the cost of establishing the above investment strategy based on the Black-Sholes model.