Three put options on a stock currently selling for $40 have the same expiration date and strike prices of $35, $40, and $45. The market prices are $5, $7, and $12 respectively. Explain how a butterfly spread can be created from these three options. Construct a table showing the payoff and profit from this strategy for different values of S_T. Sketch the profit as a function of S_T. For what values of S_T does the butterfly spread result in a loss?