Luke's quandary: to hedge or not to hedge

A little more than 10 months ago, Luke Weaver, a mortgage banker in phoenix, bought 300 shares of stock at $40 per share. Since then, the price of stock has risen to $75 per share. It is now near the end of the year, and the market is starting to weaken. Luke feels there is still plenty of play left in the stock but is afraid the tone of the market will be detrimental to his position. His wife, Denise, is taking an adult education course on the stock market and has just learned about put and call hedges. She suggest that he use puts to hedge his position. Luke is intrigued by the idea, which h discusses with his broker, who advises him that the needed puts are indeed available on his stock. Specifically, he can buy three-month puts, which 75 strike prices, at a cost of $550 each (quoted at $5.50)

Required to do:

Q1. Given the circumstances surrounding Luke's current investment position, what benefits could be derived from using the puts as a hedge device? What would be the major drawback?

Q2. What will Luck's minimum profit be if he buys three puts at the indicated option price? How much would he make if he did not hedge but instead sold his stock immediately at a price of $75 per share?

Q3. Assuming Luke uses three puts to hedge his position, indicate the amount of profit he will generate of the stock moves to $100 by the expiration date of the puts. What if the stock drops to $50 per share?

Q4. Should Lake use the puts as a hedge? Explain. Under what conditions would you urge him not to use.