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Consider the data for the four months shown below.

\begin{tabular}{lllll}
& March & April & May & June \\
\hline
Units produced & 1,251 & 1,163 & 1,250 & 1,317 \\
Labor hours & 336 & 334 & 323 & 309 \\
\end{tabular}

1. Calculate the monthly labor productivities. Do not round intermediate calculations. Round your answers to three decimal places.

\begin{tabular}{|c|c|}
\hline
Month & Productivity \\
\hline
March & \_\_\_\_ units/hour \\
April & \_\_\_\_ units/hour \\
May & \_\_\_\_ units/hour \\
June & \_\_\_\_ units/hour \\
\hline
\end{tabular}

2. Calculate the monthly productivity growths. Do not round intermediate calculations. Round your answers to two decimal places. Use a minus sign to enter a negative value, if any.

\begin{tabular}{|c|c|}
\hline
Months & Productivity growth \\
\hline
March-April & \_\_\_\_ \% \\
April-May & \_\_\_\_ \% \\
May-June & \_\_\_\_ \% \\
\hline
\end{tabular}



Answer :

GinnyAnswer
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.