You long a European put at $$20,$ and short a European put at $$10$ on a stock, both at $2-$year maturity.

$($a$)$ What is the portfolio payoff if the stock price at expiry is $$5,$$$10,$$$15,$$$20,$$$25,$ respectively?

$($b$)$ Plot the portfolio payoff at expiry as a function of the security price level at expiry.

$($c$)$ We expect the stock price to fluctuate over time, but we are sure that the stock price will stay above $$30$ as long as the company is not going bankruptcy. However, when the company does go to bankruptcy, the stock price will drop below $$2$ and will never be able to recover.

i$.$ Under these assumptions, what kind of payoff do you expect from your portfolio in all possible scenarios? $($Hint: Stock price goes to $20$ is not possible$)$

ii$.$ Can you make up another portfolio of put spreads $($long one, short the other$)$ using different strikes