The current price of a non$-$dividend paying stock is $40$ and the continuously compounded risk$-$free rate of return is $8\%.$ The following table shows call and put option premiums for three$-$month European options of various exercise prices. A trader is considering two investment strategies. The first is a long $40-$strike call and long a $40-$strike put. The second is long a $35-$strike put and long a $45-$strike call. Assume one option is on one share.

Call K$=35$

Call K$=40$

Call K$=45$ Put K$=35$

Put K$=40$

Put K$=45$

Premium $6\mathrm{.}132\mathrm{.}780\mathrm{.}970\mathrm{.}441\mathrm{.}995\mathrm{.}08$

a$)$ Please show the payoff and profit table and draw the diagram $($payoff and profit$)$ for both strategies. Assume ST is the stock price in $3-$month.

b$)$ Determine the range of stock prices in $3$ months for which the second strategy outperforms the first strategy.