Consider options on Washburn Corporation stock. There are

call options and put options, both with a strike price of $$10$ and

the expiration date of Jan. $16$th$.$ Currently the call premium is

$$0\mathrm{.}50$ and the put premium is $$1\mathrm{.}00.$ Suppose that there is a

$50\%$ chance that the stock price will be $$11$ on Jan. $16$th

$($Scenario A$)$ and another $50\%$ chance that it will be $$8$ on Jan.

$16$th $($Scenario B$).$

a$.$ Compute the gross profit and the net profit of the call

option and of the put option on Jan. $16$th under

Scenario A$,$ only for the buyer.

b$.$ Do the same under Scenario B$.$

c$.$ Now consider the following portfolio: buying one

share of the stock and buying a put option. Compute

the gross value $($excluding the premium$)$ of the

portfolio on Jan. ${16}^{th}$ under each scenario.