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 $250$ hours in any given month. The demand for billable hours for the firm over the next $6$ months is estimated$$ below:

Month

Estimate of Billable Hours

Jan.

$600$

Feb.

$510$

Mar.

$1,020$

Apr.

$1,230$

May

$650$

June

$570$

Cohen has an agreement with$$ Forrester, his former$$ partner, to help out during the busy tax$$ season, up to $250$ hours in any given month if$$ 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.

Part $2$

$$a$)$ Develop an aggregate plan for the$6-$month period $($enter your responses as whole$$ 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.

Month

Estimate of Billable Hours

CPAs

Reg. time billable hours

Reg. time cost

$"$Overtime$"$ hours

$"$Overtime$"$ cost

Forrester hours

Forrester cost

Jan.

$600$

enter your response here

enter your response here

$$$enter your response here

enter your response here

$$$enter your response here

enter your response here

$$$enter your response here