Chuck Sox makes wooden boxes in which to ship motorcycles. Chuck and his three employees invest a total of 40 hours per day making the 400 boxes. a) Their productivity $$ =10 $$ boxes/hour (round your response to two decimal places). Chuck and his employees have discussed redesigning the process to improve efficiency. Suppose they can increase the rate to 500 boxes per day. b) Their new productivity = boxes/hour (round your response to two decimal places).

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Let's break down the problem step by step.

### **a) Current Productivity**

**Given:**
- Total boxes produced per day = 400 boxes
- Total hours worked per day = 40 hours

**Productivity Calculation:**
$$
\text{Productivity} = \frac{\text{Total Boxes Produced}}{\text{Total Hours Worked}} = \frac{400 \text{ boxes}}{40 \text{ hours}} = 10 \text{ boxes/hour}
$$

**Answer:**  
Their current productivity is **10.00 boxes/hour**.

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### **b) New Productivity After Redesign**

**Given:**
- New total boxes produced per day = 500 boxes
- Total hours worked per day remains the same = 40 hours

**New Productivity Calculation:**
$$
\text{New Productivity} = \frac{\text{New Total Boxes Produced}}{\text{Total Hours Worked}} = \frac{500 \text{ boxes}}{40 \text{ hours}} = 12.50 \text{ boxes/hour}
$$

**Answer:**  
Their new productivity is **12.50 boxes/hour**.
a) Their current productivity is 10.00 boxes/hour. b) Their new productivity is 12.50 boxes/hour.

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