The price of a stock is $$80.$ The price of a one$-$year European put option on the stock with a strike price of $$70$ is quoted as $$7,$ and the price of a one$-$year European call option on the stock with a strike price of $$90$ is quoted as $$5.$

$($a$)$ Suppose that an investor buys $100$ shares, shorts $100$ call options, and buys $100$ put options.

i$.$ Please calculate the value of the portfolio within the price range given in the attached picture.

$($b$)$ How does your answer change if the investor buys $100$ shares, shorts $200$ call options, and buys $200$ put options?

i$.$ Please calculate the value of the portfolio within the price range