We will derive a two$-$state put option value in this problem. Data: $S_0=$$$100$;$x=$$$110$;$1+r=1\mathrm{.}10.$ The two possibilities for $S_T$ are $$130$ and $$80.$

Required:

a$.$ The range of $S$ is $$50$ while that of $P$ is $$30$ across the two states. What is the hedge ratio of the put?

Note: Negative value should be indicated by a minus sign. Round your answer to $2$ decimal places.

b$.$ Form a portfolio of three shares of stock and five puts. What is the $($nonrandom$)$ payoff to this portfolio? Note: Round your answer to $2$ decimal places.

$\backslash$table$[[\backslash$table$[[$Nonrandom$],[$payoff$]],$$$,354\mathrm{.}55x$