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Sagot :
Sure, let's break down each part of the question with detailed steps:
### Step-by-Step Solution for Part (a)
To complete the benefits chart, we will fill in the details for each employee position.
#### Lab Tech:
- Annual Wage: \[tex]$41,548 - Vacation Days + 9 Holidays: - There are 10 vacation days plus 9 holidays, so that's 19 days. - Unemployment Insurance (4.6% of annual wage): - \( \$[/tex]41,548 \times 0.046 = \[tex]$1,910.208 \) - FICA (6.2% of annual wage): - \( \$[/tex]41,548 \times 0.062 = \[tex]$2,575.976 \) - Medicare (1.45% of annual wage): - \( \$[/tex]41,548 \times 0.0145 = \[tex]$602.446 \) - Total Benefits: - Adding up the benefits: \( \$[/tex]1,910.208 + \[tex]$2,575.976 + \$[/tex]602.446 = \[tex]$5,089.63 \) #### Lab Analyst: - Annual Wage: \$[/tex]44,875
- Vacation Days + 9 Holidays:
- Same as lab tech, 19 days.
- Unemployment Insurance (4.6% of annual wage):
- [tex]\( \$44,875 \times 0.046 = \$2,064.25 \)[/tex]
- FICA (6.2% of annual wage):
- [tex]\( \$44,875 \times 0.062 = \$2,782.25 \)[/tex]
- Medicare (1.45% of annual wage):
- [tex]\( \$44,875 \times 0.0145 = \$650.6875 \)[/tex]
- Total Benefits:
- Adding up the benefits: [tex]\( \$2,064.25 + \$2,782.25 + \$650.6875 = \$5,497.1875 \)[/tex]
#### Receptionist:
- Annual Wage: \[tex]$16,500 - Vacation Days + 9 Holidays: - Same as others, 19 days. - Unemployment Insurance (4.6% of annual wage): - \( \$[/tex]16,500 \times 0.046 = \[tex]$759.00 \) - FICA (6.2% of annual wage): - \( \$[/tex]16,500 \times 0.062 = \[tex]$1,023.00 \) - Medicare (1.45% of annual wage): - \( \$[/tex]16,500 \times 0.0145 = \[tex]$239.25 \) - Total Benefits: - Adding up the benefits: \( \$[/tex]759.00 + \[tex]$1,023.00 + \$[/tex]239.25 = \[tex]$2,021.25 \) The completed benefits chart for Pathology Lab's staff is: \[ \begin{array}{|c|c|c|c|c|c|c|c|} \hline \textbf{Position} & \textbf{Annual Wage} & \textbf{Vacation Days + Holidays} & \textbf{Unemp. Ins. (4.6\%)} & \textbf{FICA (6.2\%)} & \textbf{Medicare (1.45\%)} & \textbf{Total Benefits} \\ \hline \text{Lab Tech} & \$[/tex]41,548 & \text{19 days} & \[tex]$1,910.208 & \$[/tex]2,575.976 & \[tex]$602.446 & \$[/tex]5,089.63 \\
\hline \text{Lab Analyst} & \[tex]$44,875 & \text{19 days} & \$[/tex]2,064.25 & \[tex]$2,782.25 & \$[/tex]650.6875 & \[tex]$5,497.1875 \\ \hline \text{Receptionist} & \$[/tex]16,500 & \text{19 days} & \[tex]$759.00 & \$[/tex]1,023.00 & \[tex]$239.25 & \$[/tex]2,021.25 \\
\hline
\end{array}
\]
### Step-by-Step Solution for Part (b)
#### Rate of Benefits for All Employees:
- Total Benefits: \[tex]$12,608.0675 - Total Wages: \$[/tex]41,548 (Lab Tech) + \[tex]$44,875 (Lab Analyst) + \$[/tex]16,500 (Receptionist) = \[tex]$102,923 - Rate of Benefits: \(\left( \frac{\text{Total Benefits}}{\text{Total Wages}} \right) \times 100\) - \( \left( \frac{ \$[/tex]12,608.0675 }{ \[tex]$102,923 } \right) \times 100 = 12.25\% \) Thus, the rate of benefits for all employees is 12.3%. ### Step-by-Step Solution for Part (c) #### Total Benefits Cost Paid by the Lab: - The total benefits that the lab pays for the employees: \$[/tex]12,608.0675
### Step-by-Step Solution for Part (d)
#### Additional Cost for a Three-Week Vacation:
- Additional Vacation Days: 15 days (3 weeks) - 10 days (2 weeks) = 5 extra days
- Annual Wage / Total Work Days:
- Lab Tech: [tex]\( \left( \frac{5}{261} \right) \times \$41,548 = \$796.69 \)[/tex]
- Lab Analyst: [tex]\( \left( \frac{5}{261} \right) \times \$44,875 = \$859.13 \)[/tex]
- Receptionist: [tex]\( \left( \frac{5}{261} \right) \times \$16,500 = \$323.47 \)[/tex]
- Total Additional Cost: [tex]\(\$796.69 + \$859.13 + \$323.47 = \$1,979.29 \)[/tex]
Thus, it would cost the lab an additional \$1,979.29 to give each employee a three-week vacation instead of two.
### Step-by-Step Solution for Part (a)
To complete the benefits chart, we will fill in the details for each employee position.
#### Lab Tech:
- Annual Wage: \[tex]$41,548 - Vacation Days + 9 Holidays: - There are 10 vacation days plus 9 holidays, so that's 19 days. - Unemployment Insurance (4.6% of annual wage): - \( \$[/tex]41,548 \times 0.046 = \[tex]$1,910.208 \) - FICA (6.2% of annual wage): - \( \$[/tex]41,548 \times 0.062 = \[tex]$2,575.976 \) - Medicare (1.45% of annual wage): - \( \$[/tex]41,548 \times 0.0145 = \[tex]$602.446 \) - Total Benefits: - Adding up the benefits: \( \$[/tex]1,910.208 + \[tex]$2,575.976 + \$[/tex]602.446 = \[tex]$5,089.63 \) #### Lab Analyst: - Annual Wage: \$[/tex]44,875
- Vacation Days + 9 Holidays:
- Same as lab tech, 19 days.
- Unemployment Insurance (4.6% of annual wage):
- [tex]\( \$44,875 \times 0.046 = \$2,064.25 \)[/tex]
- FICA (6.2% of annual wage):
- [tex]\( \$44,875 \times 0.062 = \$2,782.25 \)[/tex]
- Medicare (1.45% of annual wage):
- [tex]\( \$44,875 \times 0.0145 = \$650.6875 \)[/tex]
- Total Benefits:
- Adding up the benefits: [tex]\( \$2,064.25 + \$2,782.25 + \$650.6875 = \$5,497.1875 \)[/tex]
#### Receptionist:
- Annual Wage: \[tex]$16,500 - Vacation Days + 9 Holidays: - Same as others, 19 days. - Unemployment Insurance (4.6% of annual wage): - \( \$[/tex]16,500 \times 0.046 = \[tex]$759.00 \) - FICA (6.2% of annual wage): - \( \$[/tex]16,500 \times 0.062 = \[tex]$1,023.00 \) - Medicare (1.45% of annual wage): - \( \$[/tex]16,500 \times 0.0145 = \[tex]$239.25 \) - Total Benefits: - Adding up the benefits: \( \$[/tex]759.00 + \[tex]$1,023.00 + \$[/tex]239.25 = \[tex]$2,021.25 \) The completed benefits chart for Pathology Lab's staff is: \[ \begin{array}{|c|c|c|c|c|c|c|c|} \hline \textbf{Position} & \textbf{Annual Wage} & \textbf{Vacation Days + Holidays} & \textbf{Unemp. Ins. (4.6\%)} & \textbf{FICA (6.2\%)} & \textbf{Medicare (1.45\%)} & \textbf{Total Benefits} \\ \hline \text{Lab Tech} & \$[/tex]41,548 & \text{19 days} & \[tex]$1,910.208 & \$[/tex]2,575.976 & \[tex]$602.446 & \$[/tex]5,089.63 \\
\hline \text{Lab Analyst} & \[tex]$44,875 & \text{19 days} & \$[/tex]2,064.25 & \[tex]$2,782.25 & \$[/tex]650.6875 & \[tex]$5,497.1875 \\ \hline \text{Receptionist} & \$[/tex]16,500 & \text{19 days} & \[tex]$759.00 & \$[/tex]1,023.00 & \[tex]$239.25 & \$[/tex]2,021.25 \\
\hline
\end{array}
\]
### Step-by-Step Solution for Part (b)
#### Rate of Benefits for All Employees:
- Total Benefits: \[tex]$12,608.0675 - Total Wages: \$[/tex]41,548 (Lab Tech) + \[tex]$44,875 (Lab Analyst) + \$[/tex]16,500 (Receptionist) = \[tex]$102,923 - Rate of Benefits: \(\left( \frac{\text{Total Benefits}}{\text{Total Wages}} \right) \times 100\) - \( \left( \frac{ \$[/tex]12,608.0675 }{ \[tex]$102,923 } \right) \times 100 = 12.25\% \) Thus, the rate of benefits for all employees is 12.3%. ### Step-by-Step Solution for Part (c) #### Total Benefits Cost Paid by the Lab: - The total benefits that the lab pays for the employees: \$[/tex]12,608.0675
### Step-by-Step Solution for Part (d)
#### Additional Cost for a Three-Week Vacation:
- Additional Vacation Days: 15 days (3 weeks) - 10 days (2 weeks) = 5 extra days
- Annual Wage / Total Work Days:
- Lab Tech: [tex]\( \left( \frac{5}{261} \right) \times \$41,548 = \$796.69 \)[/tex]
- Lab Analyst: [tex]\( \left( \frac{5}{261} \right) \times \$44,875 = \$859.13 \)[/tex]
- Receptionist: [tex]\( \left( \frac{5}{261} \right) \times \$16,500 = \$323.47 \)[/tex]
- Total Additional Cost: [tex]\(\$796.69 + \$859.13 + \$323.47 = \$1,979.29 \)[/tex]
Thus, it would cost the lab an additional \$1,979.29 to give each employee a three-week vacation instead of two.
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