Disano Company, a sole proprietorship, sells only one product. The regular price is $$160.$ Variable costs are $55\%$ of this selling price, and fixed costs are $$8,400$ a month.

Management decides to decrease the selling price from $$160$ to $$145$ per unit. Assume that the cost of the product and the fixed operating expenses are not changed by this pricing decision.

$($a$)$ At the original selling price of $$160$ a unit, what is the contribution margin ratio? $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\%$

$($b$)$ At the original selling price of $$160$ a unit, what dollar volume of sales per month is required for Diana Company to break$-$even? $($Round your answer to the nearest whole dollar$)$ $$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$($c$)$ At the original selling price of $$160$ a unit, what dollar volume of sales per month is required for Diana Company to earn a monthly operating income of $$6,500?($Round your answer to the nearest whole dollar$)$ $$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$($d$)$ At the reduced selling price of $$145$ a unit, what is the contribution margin ratio? $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\%$

$($e$)$ At the reduced selling price of $$145$ a unit, what dollar volume of sales per month is required to break$-$even? $($Round your intermediate percentage to one decimal place and final answer to the nearest whole dollar$)$ $$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$($f$)$ Show the break$-$even point by extracting relevant information from the case in MS Excel.