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To help Rosa calculate the effect of a 6.25 percent increase in wages on the labor cost percentage, we can follow these steps:
### 1. Calculate Raise in Dollars for Each Week
First, determine the increase in labor costs for each week due to the wage increase from [tex]$\$[/tex]8.00[tex]$ to $[/tex]\[tex]$8.50$[/tex] per hour (a 6.25 percent increase).
- Week 1:
[tex]\[ \$10,650 \times 0.0625 = \$665.625 \][/tex]
- Week 2:
[tex]\[ \$12,075 \times 0.0625 = \$754.6875 \][/tex]
- Week 3:
[tex]\[ \$10,887 \times 0.0625 = \$680.4375 \][/tex]
- Week 4:
[tex]\[ \$10,383 \times 0.0625 = \$648.9375 \][/tex]
### 2. Calculate Total Cost of Labor for Each Week After the Raise
Next, add the raise in dollars to the original cost of labor for each week.
- Week 1:
[tex]\[ \$10,650 + \$665.625 = \$11,315.625 \][/tex]
- Week 2:
[tex]\[ \$12,075 + \$754.6875 = \$12,829.6875 \][/tex]
- Week 3:
[tex]\[ \$10,887 + \$680.4375 = \$11,567.4375 \][/tex]
- Week 4:
[tex]\[ \$10,383 + \$648.9375 = \$11,031.9375 \][/tex]
### 3. Calculate the Labor Cost Percentage for Each Week After the Raise
Now, calculate the labor cost percentage for each week after the raise:
- Week 1:
[tex]\[ \left( \frac{\$11,315.625}{\$27,600} \right) \times 100 \approx 40.9986\% \][/tex]
- Week 2:
[tex]\[ \left( \frac{\$12,829.6875}{\$32,250} \right) \times 100 \approx 39.7820\% \][/tex]
- Week 3:
[tex]\[ \left( \frac{\$11,567.4375}{\$28,650} \right) \times 100 \approx 40.3750\% \][/tex]
- Week 4:
[tex]\[ \left( \frac{\$11,031.9375}{\$37,200} \right) \times 100 \approx 29.6557\% \][/tex]
### 4. Calculate Totals and Average Labor Cost Percentage
Finally, compute the totals and average labor cost percentage.
- Total Original Cost of Labor:
[tex]\[ \$10,650 + \$12,075 + \$10,887 + \$10,383 = \$43,995 \][/tex]
- Total Raise in Dollars:
[tex]\[ \$665.625 + \$754.6875 + \$680.4375 + \$648.9375 = \$2,749.6875 \][/tex]
- Total Cost of Labor After Raise:
[tex]\[ \$11,315.625 + \$12,829.6875 + \$11,567.4375 + \$11,031.9375 = \$46,744.6875 \][/tex]
- Total Sales:
[tex]\[ \$27,600 + \$32,250 + \$28,650 + \$37,200 = \$125,700 \][/tex]
- Average Labor Cost Percentage:
[tex]\[ \left( \frac{\$46,744.6875}{\$125,700} \right) \times 100 = 37.1875\% \][/tex]
### Tabulated Results:
[tex]\[ \begin{array}{|l|r|r|r|r|r|} \hline \text{Week} & \text{Original Cost of Labor} & \text{Raise in Dollars} & \text{Total Cost of Labor} & \text{Sales} & \text{Labor Cost \%} \\ \hline 1 & \$10,650 & \$665.625 & \$11,315.625 & \$27,600 & 40.9986\% \\ \hline 2 & \$12,075 & \$754.6875 & \$12,829.6875 & \$32,250 & 39.7820\% \\ \hline 3 & \$10,887 & \$680.4375 & \$11,567.4375 & \$28,650 & 40.3750\% \\ \hline 4 & \$10,383 & \$648.9375 & \$11,031.9375 & \$37,200 & 29.6557\% \\ \hline \text{Total} & \$43,995 & \$2,749.6875 & \$46,744.6875 & \$125,700 & \text{37.1875\%} \\ \hline \end{array} \][/tex]
From the calculations above, raising the hourly wage results in an increase in labor costs percentage to an average of 37.1875%, which is within Rosa's acceptable limit of 38%.
### 1. Calculate Raise in Dollars for Each Week
First, determine the increase in labor costs for each week due to the wage increase from [tex]$\$[/tex]8.00[tex]$ to $[/tex]\[tex]$8.50$[/tex] per hour (a 6.25 percent increase).
- Week 1:
[tex]\[ \$10,650 \times 0.0625 = \$665.625 \][/tex]
- Week 2:
[tex]\[ \$12,075 \times 0.0625 = \$754.6875 \][/tex]
- Week 3:
[tex]\[ \$10,887 \times 0.0625 = \$680.4375 \][/tex]
- Week 4:
[tex]\[ \$10,383 \times 0.0625 = \$648.9375 \][/tex]
### 2. Calculate Total Cost of Labor for Each Week After the Raise
Next, add the raise in dollars to the original cost of labor for each week.
- Week 1:
[tex]\[ \$10,650 + \$665.625 = \$11,315.625 \][/tex]
- Week 2:
[tex]\[ \$12,075 + \$754.6875 = \$12,829.6875 \][/tex]
- Week 3:
[tex]\[ \$10,887 + \$680.4375 = \$11,567.4375 \][/tex]
- Week 4:
[tex]\[ \$10,383 + \$648.9375 = \$11,031.9375 \][/tex]
### 3. Calculate the Labor Cost Percentage for Each Week After the Raise
Now, calculate the labor cost percentage for each week after the raise:
- Week 1:
[tex]\[ \left( \frac{\$11,315.625}{\$27,600} \right) \times 100 \approx 40.9986\% \][/tex]
- Week 2:
[tex]\[ \left( \frac{\$12,829.6875}{\$32,250} \right) \times 100 \approx 39.7820\% \][/tex]
- Week 3:
[tex]\[ \left( \frac{\$11,567.4375}{\$28,650} \right) \times 100 \approx 40.3750\% \][/tex]
- Week 4:
[tex]\[ \left( \frac{\$11,031.9375}{\$37,200} \right) \times 100 \approx 29.6557\% \][/tex]
### 4. Calculate Totals and Average Labor Cost Percentage
Finally, compute the totals and average labor cost percentage.
- Total Original Cost of Labor:
[tex]\[ \$10,650 + \$12,075 + \$10,887 + \$10,383 = \$43,995 \][/tex]
- Total Raise in Dollars:
[tex]\[ \$665.625 + \$754.6875 + \$680.4375 + \$648.9375 = \$2,749.6875 \][/tex]
- Total Cost of Labor After Raise:
[tex]\[ \$11,315.625 + \$12,829.6875 + \$11,567.4375 + \$11,031.9375 = \$46,744.6875 \][/tex]
- Total Sales:
[tex]\[ \$27,600 + \$32,250 + \$28,650 + \$37,200 = \$125,700 \][/tex]
- Average Labor Cost Percentage:
[tex]\[ \left( \frac{\$46,744.6875}{\$125,700} \right) \times 100 = 37.1875\% \][/tex]
### Tabulated Results:
[tex]\[ \begin{array}{|l|r|r|r|r|r|} \hline \text{Week} & \text{Original Cost of Labor} & \text{Raise in Dollars} & \text{Total Cost of Labor} & \text{Sales} & \text{Labor Cost \%} \\ \hline 1 & \$10,650 & \$665.625 & \$11,315.625 & \$27,600 & 40.9986\% \\ \hline 2 & \$12,075 & \$754.6875 & \$12,829.6875 & \$32,250 & 39.7820\% \\ \hline 3 & \$10,887 & \$680.4375 & \$11,567.4375 & \$28,650 & 40.3750\% \\ \hline 4 & \$10,383 & \$648.9375 & \$11,031.9375 & \$37,200 & 29.6557\% \\ \hline \text{Total} & \$43,995 & \$2,749.6875 & \$46,744.6875 & \$125,700 & \text{37.1875\%} \\ \hline \end{array} \][/tex]
From the calculations above, raising the hourly wage results in an increase in labor costs percentage to an average of 37.1875%, which is within Rosa's acceptable limit of 38%.
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