A trader creates a long strangle with put options with a strike price of $90 per share, and call options with a strike of $105 per share by trading a total of 40 option contracts (buy 20 put contracts and buy 20 call contracts). Each contract is written on 100 shares of stock. The put option is worth $10.5 per share, and the call option is worth $6.5 per share. a) What is the value of the strangle at maturity as a function of the then stock price? b) What is the profit of the strangle at maturity as a function of the then stock price? Make sure to derive the exact range of then stock prices where the trade is profitable.