To calculate the category expense contribution for payroll, we will follow these steps:
1. Calculate the total expenses:
We need to sum up all the expenses from different categories.
[tex]\[
\begin{align*}
\text{Total expenses} &= \text{Payroll} + \text{Advertising} + \text{Raw Materials} + \text{Rent} + \text{Insurance} + \text{Utilities} + \text{Services} \\
&= \$ 393,110 + \$ 8,252 + \$ 224,250 + \$ 41,345 + \$ 8,010 + \$ 12,500 + \$ 7,250 \\
&= \$ 694,717
\end{align*}
\][/tex]
2. Calculate the contribution percentage for payroll:
We find the percentage contribution of the payroll category by dividing the payroll expense by the total expenses and then multiplying by 100 to convert it to a percentage.
[tex]\[
\begin{align*}
\text{Payroll percentage} &= \left( \frac{\text{Payroll}}{\text{Total expenses}} \right) \times 100 \\
&= \left( \frac{\$ 393,110}{\$ 694,717} \right) \times 100 \\
&\approx 56.58563127143859 \%
\end{align*}
\][/tex]
3. Round to the nearest whole percent:
Finally, we round the percentage to the nearest whole number.
[tex]\[
\text{Payroll percentage (rounded)} \approx 57 \%
\][/tex]
Therefore, the contribution of payroll to the annual expenses, rounded to the nearest whole percent, is [tex]\( 57 \% \)[/tex].
