A put option in finance allows you to sell a share of stock at a given price in the future. There are different types of put optionsA European put option allows you to sell a share of stock at a given price, called the exercise price, at a particular point in time after the purchase of the option. For example, suppose you purchase a six$-$month European put option for a share of stock with an exercise price of $$26.$ If six months later, the stock price per share is $$26$ or more, the option has no value. If in six months the stock price is lower than $$26$ per share, then you can purchase the stock and immediately sell it at the higher exercise price of $$26$If the price per share in six months is $$22\mathrm{.}50,$ you can purchase a share of the stock for $$22\mathrm{.}50$ and then use the put option to immediately sell the share for $$26.$ Your profit would be the difference, $526-522\mathrm{.}5=53\mathrm{.}5$ per share, less the cost of the option. If you paid $$1\mathrm{.}00$ per put option, then your profit would be $\backslash$$$3\mathrm{.}50-\backslash$$$1\mathrm{.}00=\backslash$$$2\mathrm{.}50$ per share. The point of purchasing a European option is to limit the risk of a decrease in the per$-$share price of the stock. Suppose you purchased $200$ shares of the stock at $ $28$ per share and $90$ six$-$month European put options with an exercise price of $$26$Each put option costs $$1.($ a$)$ Using data tables, construct a model that shows the value of the portfolio with options and without options for a share price in six months between $$20$ and $ $29$ per share in increments of $$1\mathrm{.}00.$ What is the benefit of the put options on the portfolio value for the different share prices? For subtractive or negative numbers use a minus sign even if there is a $+$ sign before the blank $($Example: $-300).$ If your answer is zero, enter $"($a$)$ Using data tables, construct a model that shows the value of the portfolio with options and without options for a share price in six months between $$20$ and $$29$ per share in increments of $$1\mathrm{.}00.$ What is the benefit of the put options on the portfolio value for the different share prices? For subtractive or negative numbers use a minus sign even if there is a $+$ sign before the blank $($Example: $-300).$ If your answer is zero, enter $"0".$

$\backslash$table$[[$Share Price,Benefit of Options$],[$$$20,$$