A trader creates a bear spread by selling a six$-$month put option with a $$25$ strike price for $$2\mathrm{.}15$ and

buying a six$-$month put option with a $$29$ strike price for $$4\mathrm{.}75.$ What is the initial investment? What is

the total payoff when the stock price in six months is $($a$)$ $$23,($b$)$ $$28,$ and $($c$)$ $$33.$