Draw well-labelled diagrams showing the payoffs for the following investments as a function of the price of the stock index at maturity. Assume throughout that the priceof each option contract is $5 and that one option contract is for one unit of investmentin the index. (a) Buy the index and sell a call at strike price $100. (b) Buy a put at strike price $90 and buy a call at strike price $110. (c) Buy a call at strike price $95 and sell a call at strike price $105. (d) Buy a call and sell a put at strike price $100 on the index