There is a stock X whose initial price is X0 = $55. A call option with expiration date T and strike price $50 has initial price $7.50, and a put option with expiration date T and strike price $60 has initial price $4. You create a portfolio Z by selling short 100 shares of X and using the proceeds to by 500 of the call options described above, and a number of the put options described above in order to make the initial value Z0 of your portfolio equal to zero.

1.) How many of the put options do you buy?

(i got 437.5)

2.) Plot the value ZT of the portfolio at time T as a function of the stock price XT at that time. In other words, draw a graph with XT on the horizontal axis and ZT on the vertical axis. consider separately the cases ST < 50, 50 < ST < 60 and ST > 60.

3.)For what values of XT is the value of the portfolio equal to zero at time T? For what values of XT is the value of the portfolio positive at time T? For what values of XT is the value of the portfolio negative at time T?

please explain

thanks