Forrester and Cohen is a small accounting firm, managed by Joseph Cohen since the retirement in December of his partner Brad Forrester. Cohen and his $3$ CPAs together bill $620$ hours per month. When Cohen or another accountant bills more than $155$ hours per month, he or she gets an additional "overtime" pay of $$63\mathrm{.}20$ for each of the extra hours: this is above and beyond the $$4,900$ salary each draws during the month. $($Cohen draws the same base pay as his employees.$)$ Cohen strongly discourages any CPA from working $($billing$)$ more than $245$ hours in any given month. The demand for billable hours for the firm over the next $6$ months is estimated below:

$\backslash$table$[[$Month$,$Estimate of Billable Hours$],[$Jan$.,600],[$Feb$.,490],[$Mar$.,1,010],[$Apr$.,1,210],[$May$,650],[$June$,570]]$

Cohen has an agreement with Forrester, his former partner, to help out during the busy tax season, up to $245$ hours in any given month if needed, for an hourly fee of $$135.$ Cohen will not even consider laying off one of his colleagues in the case of a slow economy. He could, however, hire another CPA at the same salary, as business dictates.

a$)$ Develop an aggregate plan for the $6-$month period $($enter your responses as whole numbers$).$ Use regular time, then overtime, then Forrester, and then hire additional CPAs if needed.

Note: For the CPA column, only include Cohen, his $3$ CPAs, and any new CPAs he may hire in your total. Do NOT include Forrester.

$\backslash$table$[[$Month$,\backslash$table$[[$Estimate of$],[$Billable$],[$Hours$]],$CPAs,$\backslash$table$[[$Reg$.$ time$],[$billable$],[$hours$]],\backslash$table$[[$Reg$.$ time$],[$cost$]],\backslash$table$[["$Overtime$"],[$hours$]],\backslash$table$[["$Overtime$"],[$cost$]],\backslash$table$[[$Forrester$],[$hours$]],\backslash$table$[[$Forrester$],[$cost$]]],[$Jan$.,600,,,$$$,,$$$,,$$