You have been asked to manage a portfolio of call options on a stock. you are given the following information:

Time to expiration = 1 year.

You have purchased 10 call options with K = 30

You are to take long or short positions in call options with K = 35 and call options with k = 45 so that the total payoff of your combined option portfolio at expiration is zero if the stock is trading at or greater than 45 at expiration (the combined payoff from the 10 call options with k = 30 that you already own together with whatever long or short positions you take in 35 and 45 strike calls is equal to zero for s1 > 45).

a) what long or short position in each of the call options with strike 35 and call options with strike 45 is needed?

b) draw payoff diagram. making sure to clearly label the maximum payoff for the option in the portfolio