Amy owns $100$ shares of ABC stock with a cost basis of $$35$ a share. The stock is currently trading at $$54$ a share. Amy believes the price of ABC stock will fall to $$45$ a share in the near future but over the longer term of $3$ to $5$ years, increase in value to $$75$ a share. Amy would like to benefit from the expected near$-$term decline if it occurs. Therefore, Amy writes a covered call at a strike price of $$55$ and a premium of $$2.$

$($a$)$ How will the covered call help Amy profit if the expected phice decline occurs?

$($b$)$ What is the best$-$case scenario for?

$($c$)$ What is the maximum profit Amy can incur from the call itself $($ignoring the stock$)?$