Answer :
Sure, let's solve this step-by-step:
### Problem 1:
Five employees, who each work 8 hours per day, are able to produce 80 units. We need to determine their productivity per hour.
1. Total hours worked by all employees in a day:
[tex]\[
\text{Total hours} = \text{Number of employees} \times \text{Hours per day} = 5 \times 8 = 40 \text{ hours}
\][/tex]
2. Productivity per hour:
[tex]\[
\text{Productivity per hour} = \frac{\text{Total units produced}}{\text{Total hours worked}} = \frac{80 \text{ units}}{40 \text{ hours}} = 2 \text{ units per hour}
\][/tex]
### Problem 2:
The manufacturing process is redesigned to be more efficient, and now the five employees can produce 100 units per day.
#### Part a) New productivity per hour:
1. Total hours worked by all employees in a day remains the same (40 hours).
2. New productivity per hour:
[tex]\[
\text{New productivity per hour} = \frac{\text{Total units produced}}{\text{Total hours worked}} = \frac{100 \text{ units}}{40 \text{ hours}} = 2.5 \text{ units per hour}
\][/tex]
#### Part b) Per unit increase in productivity per hour:
[tex]\[
\text{Increase in productivity per hour} = \text{New productivity per hour} - \text{Initial productivity per hour} = 2.5 \text{ units per hour} - 2 \text{ units per hour} = 0.5 \text{ units per hour}
\][/tex]
#### Part c) Percentage change in productivity:
[tex]\[
\text{Percentage change in productivity} = \left( \frac{\text{Increase in productivity per hour}}{\text{Initial productivity per hour}} \right) \times 100 = \left( \frac{0.5}{2} \right) \times 100 = 25\%
\][/tex]
### Summary:
1. Productivity per hour (initial): 2 units per hour.
2. New productivity per hour: 2.5 units per hour.
3. Increase in productivity per hour: 0.5 units per hour.
4. Percentage change in productivity: 25%.
### Problem 1:
Five employees, who each work 8 hours per day, are able to produce 80 units. We need to determine their productivity per hour.
1. Total hours worked by all employees in a day:
[tex]\[
\text{Total hours} = \text{Number of employees} \times \text{Hours per day} = 5 \times 8 = 40 \text{ hours}
\][/tex]
2. Productivity per hour:
[tex]\[
\text{Productivity per hour} = \frac{\text{Total units produced}}{\text{Total hours worked}} = \frac{80 \text{ units}}{40 \text{ hours}} = 2 \text{ units per hour}
\][/tex]
### Problem 2:
The manufacturing process is redesigned to be more efficient, and now the five employees can produce 100 units per day.
#### Part a) New productivity per hour:
1. Total hours worked by all employees in a day remains the same (40 hours).
2. New productivity per hour:
[tex]\[
\text{New productivity per hour} = \frac{\text{Total units produced}}{\text{Total hours worked}} = \frac{100 \text{ units}}{40 \text{ hours}} = 2.5 \text{ units per hour}
\][/tex]
#### Part b) Per unit increase in productivity per hour:
[tex]\[
\text{Increase in productivity per hour} = \text{New productivity per hour} - \text{Initial productivity per hour} = 2.5 \text{ units per hour} - 2 \text{ units per hour} = 0.5 \text{ units per hour}
\][/tex]
#### Part c) Percentage change in productivity:
[tex]\[
\text{Percentage change in productivity} = \left( \frac{\text{Increase in productivity per hour}}{\text{Initial productivity per hour}} \right) \times 100 = \left( \frac{0.5}{2} \right) \times 100 = 25\%
\][/tex]
### Summary:
1. Productivity per hour (initial): 2 units per hour.
2. New productivity per hour: 2.5 units per hour.
3. Increase in productivity per hour: 0.5 units per hour.
4. Percentage change in productivity: 25%.
