Demand for doughnut holes on Saturdays at Don$$s Doughnut Shoppe is shown in the following table.

Demand

$($dozens$)$ Relative

Frequency Demand

$($dozens$)$ Relative

Frequency

$19\mathrm{.}0325\mathrm{.}12$

$20\mathrm{.}0526\mathrm{.}13$

$21\mathrm{.}1627\mathrm{.}08$

$22\mathrm{.}0428\mathrm{.}04$

$23\mathrm{.}1029\mathrm{.}09$

$24\mathrm{.}16$

Click here for the Excel Data File

a$-1.$ Determine the optimal number of doughnut holes, in dozens, to stock if labor, materials, and overhead are estimated to be $$5\mathrm{.}80$ per dozen, doughnut holes are sold for $$7\mathrm{.}40$ per dozen, and leftover doughnut holes at the end of each day are sold the next day at half price.