A portfolio manager in charge of a portfolio worth $50 million is concerned that the market might decline rapidly during the next six months and would like to use options on the S&P 100 to provide protection against the portfolio falling below$45 million. The S&P 100 index is currently standing at 3000 and each contract is on 100 times the index. a. If the portfolio has a beta of 1.0, how many put options should be purchased? b. If the portfolio has a beta of 1.0, what should the strike prices of the put options be?