Which company is more productive overall and by how much?
Understand the Problem
The question is asking to determine which contracting company (Archer or Bronson) is more productive based on the distance of roadway repaved, the number of employees, days worked, and costs incurred. We will calculate productivity for both companies considering the distance repaved per employee per day.
Answer
Archer is more productive if $2.5 \text{ km per employee per day} > 1.5 \text{ km per employee per day}$.
Answer for screen readers
The answer will depend on the specific values used for the distances, employee counts, and number of days worked.
If we assume:
- Archer repaved 500 km, with 10 employees, and worked for 20 days:
$$ \text{Productivity}_A = \frac{500}{10 \times 20} = \frac{500}{200} = 2.5 \text{ km per employee per day} $$
- Bronson repaved 300 km, with 8 employees, and worked for 25 days:
$$ \text{Productivity}_B = \frac{300}{8 \times 25} = \frac{300}{200} = 1.5 \text{ km per employee per day} $$
Then, Archer is more productive.
Steps to Solve
- Calculate Productivity for Archer
To find Archer's productivity, we need to gather the following data:
- Distance repaved by Archer (let's say it is $D_A$ kilometers)
- Number of employees working for Archer ($E_A$)
- Days worked by Archer ($D_W$)
The productivity formula is:
$$ \text{Productivity}_A = \frac{D_A}{E_A \times D_W} $$
Insert the values for distance, number of employees, and days worked to find the productivity.
- Calculate Productivity for Bronson
Now, we will calculate the productivity for Bronson using similar data:
- Distance repaved by Bronson (let's say it is $D_B$ kilometers)
- Number of employees working for Bronson ($E_B$)
- Days worked by Bronson ($D_W$)
Apply the same productivity formula:
$$ \text{Productivity}_B = \frac{D_B}{E_B \times D_W} $$
Insert the values for distance, number of employees, and days worked for Bronson.
- Compare the Productivity Values
Once we have calculated both productivity values, compare them to determine which company is more productive:
If $\text{Productivity}_A > \text{Productivity}_B$, then Archer is more productive.
If $\text{Productivity}_B > \text{Productivity}_A$, then Bronson is more productive.
- Conclude the Analysis
Make a final statement based on the comparison. For example, if Archer's productivity is greater, state, "Archer is the more productive company, repaving more kilometers per employee per day than Bronson."
The answer will depend on the specific values used for the distances, employee counts, and number of days worked.
If we assume:
- Archer repaved 500 km, with 10 employees, and worked for 20 days:
$$ \text{Productivity}_A = \frac{500}{10 \times 20} = \frac{500}{200} = 2.5 \text{ km per employee per day} $$
- Bronson repaved 300 km, with 8 employees, and worked for 25 days:
$$ \text{Productivity}_B = \frac{300}{8 \times 25} = \frac{300}{200} = 1.5 \text{ km per employee per day} $$
Then, Archer is more productive.
More Information
Productivity analysis is important in many industries to understand resource utilization and efficiency. Companies often use these calculations to improve their operations and make informed decisions regarding staffing and project management.
Tips
- Not using the correct values: Make sure you input the correct distance repaved, number of employees, and days worked.
- Confusing the productivity formula: Remember that productivity is the distance divided by the product of employees and days worked.
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