$15-$ Duke Metal Works produces two types of metal lamps. Duke manufactures $24,640$ basic lamps and $6,250$ designer lamps. Its activity$-$based costing system uses two indirect$-$cost pools. One cost pool is for set up costs and the other for general manufacturing overhead. Duke allocates set up costs to the two lamps based on setuplabor$-$hours and general manufacturing overhead costs on the basis of direct manufacturing labor$-$hours. It provides the following budgeted cost information:

$\backslash$table$[[,$Basic Lamps,Designer Lamps,,Total$],[$Direct materials per lamp,$$,12,,],[$Direct manufacturing labor$-$hours per lamp,$0\mathrm{.}4$ hours,$0\mathrm{.}5$ hours,,$],[$Direct manufacturing labor rate per hour,$30,30,,],[$Setup costs,,,$$,130,800],[$Lamps produced per batch,$320,50,,],[$Setup$-$hours per batch,$1$ hour,$2$ hours,,$],[$General manufacturing overhead costs,,,S$,102,858]]$

$2-$ Calculate the unit cost of the basic lamps using Duke's activity$-$based costing system.

$1-$ Calculate the unit cost of the designer lamps using Duke's activity$-$based costing system.