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1. Five employees, who each work 8 hours per day, are able to produce 80 units. What is their productivity per hour?

2. Using the information from problem 1, the manufacturing process is redesigned to be more efficient. As a result, the five employees are now able to produce 100 units per day.

a) What is the new productivity per hour?

b) What is the per unit increase in productivity per hour?

c) What is the percentage change in productivity?

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%.

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