$($a$)$ AquaFresh markets a simple water control and timer that it mass$$produces$.$ Last year, the company sold $696,000$ units at an average unit selling price of $$4\mathrm{.}20.$ The variable costs were $$1,900,080,$ and the fixed costs were $$683,256.$

$1.$ What is the product's contribution margin ratio? $($Round to nearest whole percentage$)$

$2.$ What is the company's break$$even point in sales units and in sales dollars for this

product?

$3.$ What is the margin of safety, both in dollars and as a ratio? $($Round to nearest whole percentage$)$

$4.$ If management wanted to increase its income from this product by $10\%,$ how many additional units would have to be sold to reach this income level?

$5.$ If sales increase by $51,000$ units and the cost behaviors do not change, how much will income increase on this product?

$($b$)$ AquaFresh is thinking of mass$$producing one of its special$$order sprinklers. To do so would increase unit variable costs for all sprinklers by an average of $$0\mathrm{.}70.$ The company also estimates that this change could increase the overall number of sprinklers sold by $10\%,$ and the average unit sales price would increase $$0\mathrm{.}20.$ AquaFresh currently sells $491,740$ sprinkler units at an average unit selling price of $$26\mathrm{.}50.$ The manufacturing costs are $$6,863,512$ variable and $$2,050,140$ fixed. Selling and administrative costs are $$2,651,657$ variable and $$794,950$ fixed.

$1.$ If AquaFresh begins mass$$producing its special$$order sprinklers, how would this affect the company?

$2.$ If the average unit sales price per sprinkler did not increase when the company began mass$$producing the special$$order sprinkler, what would be the effect on the company?