Question #$7$: Option Strategies $[12$ Points$]$

The common stock of Lancaster Colony Corporation $($LANC$)$ has been trading in a narrow range around $$175$ per share for months, and you believe that there is a good chance that there will be volatility in the stock over the next three months. The price of a three$-$month put option with a strike price of $$175$ is $$4\mathrm{.}50,$ and a call with the same expiration date and exercise price sells for $$3\mathrm{.}15.$

$($a$)$ What would be a simple options strategy using a put and a call to exploit your conviction about the stock price's future movement? What would be the cost to purchase this strategy? $[4$ Points$]$

$($b$)$ What are the break even stock prices for an investor who employs the strategy identified in Part $($a$)?$

$[4$ Points$]$

$($c$)$ What is the maximum possible loss an investor can suffer from this strategy? $[4$ Points$]$