Mee Inc. manufactures phone batteries. The following activity information is available for its batteries:

$\backslash$table$[[$Activity$,\backslash$table$[[$Activity$-$based usage$],[($hours per unit$)]],$Activity rate per hour,Activity cost$],[$Assembly$,0\mathrm{.}75,16,12\mathrm{.}00],[$Setup$,0\mathrm{.}25,18,4\mathrm{.}50],[$Production control,$0\mathrm{.}25,34,8\mathrm{.}50],[$Materials control,$0\mathrm{.}10,30,3\mathrm{.}00],[$Moving$,0\mathrm{.}30,14,4\mathrm{.}20],[$Testing$,0\mathrm{.}30,21,6\mathrm{.}30],[$Activity cost per unit,,,$38\mathrm{.}50]]$

production control required one$-$fourth less time to complete per unit and the testing time was reduced by half.

Based on the data, identify the correct statement.

a$.$ These process improvements reduced the activity cost of each battery from $$38\mathrm{.}50$ to $$33\mathrm{.}23,$ or $$5\mathrm{.}28,$ thus exceeding the $$4\mathrm{.}00$ target.

b$.$ These process improvements reduced the activity cost of each battery from $$38\mathrm{.}50$ to $$34\mathrm{.}23,$ or $$4\mathrm{.}28,$ thus exceeding the $$4\mathrm{.}00$ target.

c$.$ These process improvements reduced the activity cost of each battery from $$38\mathrm{.}50$ to $$35\mathrm{.}44,$ or $$3\mathrm{.}06,$ thus not exceeding the $$4\mathrm{.}00$ target.

d$.$ These process improvements reduced the activity cost of each battery from $$38\mathrm{.}50$ to $$36\mathrm{.}21,$ or $$2\mathrm{.}29,$ thus not exceeding the $$4\mathrm{.}00$ target.