Forrester and Cohen is a small accounting$$ firm, managed by Joseph Cohen since the retirement in December of his partner Brad Forrester. Cohen and his $3$ CPAs together bill $640$ hours per month. When Cohen or another accountant bills more than $160$ hours per$$ month, he or she gets an additional$$ "overtime" pay of $$$$63\mathrm{.}80$ for each of the extra$$ hours: this is above and beyond the $$$$5,100$ salary each draws during the month.$($Cohen draws the same base pay as his$$ employees.$)$ Cohen strongly discourages any CPA from working$($billing$)$ more than $255$ 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.

$490$

Mar.

$1,010$

Apr.

$1,230$

May

$650$

June

$570$

Cohen has an agreement with$$ Forrester, his former$$ partner, to help out during the busy tax$$ season, up to $255$ hours in any given month if$$ needed, for an hourly fee of $$$$120.$ Cohen will not even consider laying off one of his colleagues in the case of a slow economy. He$$ 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.

$600$

$44$

$640640$

$$$$20,40020,400$

$00$

$$$$00$

$00$

$$$$00$

Part $3$

Feb.

$490$

$44$

$640640$

$$$$20,40020,400$

$00$

$$$$00$

$00$

$$$$00$

Part $4$

Mar.

$1,010$

$44$

$640640$

$$$$20,40020,400$

$370370$

$$$$23,60623,606$

$00$

$$$$00$

Part $5$

Apr.

$1,230$

$44$

$640640$

$$$$2040020400$

$380380$

$$$$24,24424,244$

$210210$

$$$$25,20025,200$

Part $6$

May

$650$

$44$

$640640$

$$$$2040020400$

$1010$

$$$$638638$

$00$

$$$$00$

Part $7$

June

$570$

$44$

$640640$

$$$$2040020400$

$00$

$$$$00$

$00$

$$$$00$

Part $8$

$$b$)$ Compute the cost of$$ Cohen's plan of using overtime and Forrester.

The cost of$$ Cohen's plan is $$$enter your response here $($enter your response as a whole$$ number$).$