The Shirt Works sells a large variety of tee shirts and sweatshirts. Steve Hooper, the owner, is thinking of expanding his sales by hiring high school students, on a commission basis, to sell sweatshirts bearing the name and mascot of the local high school.

These sweatshirts would have to be ordered from the manufacturer six weeks in advance, and they could not be returned because of the unique printing required. The sweatshirts would cost Hooper $$19\mathrm{.}00$ each with a minimum order of $224$ sweatshirts. Any additional sweatshirts would have to be ordered in increments of $224.$

Since Hooper$$s plan would not require any additional facilities, the only costs associated with the project would be the costs of the sweatshirts and the costs of the sales commissions. The selling price of the sweatshirts would be $$38\mathrm{.}00$ each. Hooper would pay the students a commission of $$6\mathrm{.}00$ for each shirt sold.

Required:

$1.$ What level of unit sales and dollar sales is needed to attain a target profit of $$11,648?$

$2.$ Assume that Hooper places an initial order for $224$ sweatshirts. What is his break$-$even point in unit sales and dollar sales? $($Round your intermediate calculations, round "Break$-$even point in unit sales" up to the nearest whole unit and round "Break$-$even point in dollar sales" to the nearest whole dollar.$)$

$3.$ How many sweatshirts would Hooper need to sell to earn a target profit of $$13,104?($Round final answer up to the nearest whole unit.$)$