To address the problem, we will start by calculating the monthly labor productivities for March, April, May, and June. The formula for productivity is:
[tex]\[
\text{Productivity} = \frac{\text{Units produced}}{\text{Labor hours}}
\][/tex]
We will then determine the monthly productivity growths, where the growth from one month to the next is given by:
[tex]\[
\text{Productivity Growth} = \left( \frac{\text{New productivity} - \text{Old productivity}}{\text{Old productivity}} \right) \times 100
\][/tex]
Let's proceed step by step:
### Step 1: Calculate Monthly Labor Productivities
1. March:
[tex]\[
\text{Productivity} = \frac{1251}{336} \approx 3.723
\][/tex]
2. April:
[tex]\[
\text{Productivity} = \frac{1163}{334} \approx 3.482
\][/tex]
3. May:
[tex]\[
\text{Productivity} = \frac{1250}{323} \approx 3.870
\][/tex]
4. June:
[tex]\[
\text{Productivity} = \frac{1317}{309} \approx 4.262
\][/tex]
Summarizing these into a table:
\begin{tabular}{|c|c|}
\hline
Month & Productivity \\
\hline
March & 3.723 units/hour \\
\hline
April & 3.482 units/hour \\
\hline
May & 3.870 units/hour \\
\hline
June & 4.262 units/hour \\
\hline
\end{tabular}
### Step 2: Calculate Monthly Productivity Growths
1. March to April:
[tex]\[
\text{Productivity Growth} = \left( \frac{3.482 - 3.723}{3.723} \right) \times 100 \approx -6.48\%
\][/tex]
2. April to May:
[tex]\[
\text{Productivity Growth} = \left( \frac{3.870 - 3.482}{3.482} \right) \times 100 \approx 11.14\%
\][/tex]
3. May to June:
[tex]\[
\text{Productivity Growth} = \left( \frac{4.262 - 3.870}{3.870} \right) \times 100 \approx 10.13\%
\][/tex]
Summarizing these into a table:
\begin{tabular}{|c|c|}
\hline
Months & Productivity growth \\
\hline
March-April & -6.48\% \\
\hline
April-May & 11.14\% \\
\hline
May-June & 10.13\% \\
\hline
\end{tabular}
This completes our analysis of the labor productivities and the monthly productivity growths for the given data.
