Par Putters Company sells golf balls for $$26$ per dozen. The store's overhead expenses are $32\%$ of cost and the owners require a profit of $22\%$ of cost$.$

$($a$)$ For how much does Par Putters Company buy one dozen golf balls?

$($b$)$ What is the price needed to cover all of the costs and expenses?

$($c$)$ What is the highest rate of markdown at which the store will still break even?

$($d$)$ What is the highest rate of discount that can be advertised without incurring an absolute loss?

$($a$)$ The cost of one dozen golf balls is $

$($Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.$)$

$($b$)$ The price needed to cover all of the costs and expenses is $ per dozen.

$($Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.$)$

$($c$)$ The highest rate of markdown is $\%.$

$($Round the final answer to two decimal places as needed. Round all intermediate values to six decimal places as needed.$)$

$($d$)$ The highest rate of discount is $\%.$

$($Round the final answer to two decimal places as needed. Round all intermediate values to six decimal places as needed.$)$