Health $\text{'}$S Us$,$ Inc., uses a traditional product costing system to assign overhead costs uniformly to all its packaged multigrain products. To meet Food and Drug Administration requirements and to assure its customers of safe, sanitary, and nutritious food, Health $\text{'}$S Us engages in a high level of quality control. Health $\text{'}$S Us assigns its quality$-$control overhead costs to all products at a rate of $17\%$ of direct labor costs. Its direct labor cost for the month of June for its low$-$calorie breakfast line is $$70,500.$ In response to repeated requests from its financial vice president, Health $\text{'}$S Us's management agrees to adopt activity$-$based costing. Data relating to the lowcalorie breakfast line for the month of June are as follows.

$\backslash$table$[[$Activity Cost Pools,Cost Drivers,$\backslash$table$[[$Overhead$],[$Rate$]],\backslash$table$[[$Number of Cost Drivers$],[$Used per Activity$]]],[$Inspections of material received,Number of pounds,$$0\mathrm{.}90$ per pound,$5,900$ pounds$],[$In$-$process inspections,Number of servings,$$0\mathrm{.}33$ per serving,$11,000$ servings$],[$FDA certification,Customer orders,$$12\mathrm{.}00$ per order,$450$ orders$]]$

$($a$)$

Compute the quality$-$control overhead cost to be assigned to the low$-$calorie breakfast product line for the month of June $(1)$ using the traditional product costing system $($direct labor cost is the cost driver$),$ and $(2)$ using activity$-$based costing.