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 \( =\square \) boxes/hour (round your response to two decimal places).

To determine the new productivity after redesigning the process, let's break down the problem step by step. ### **Initial Scenario:** - **Total Hours Worked per Day:** 40 hours - **Total Boxes Produced per Day:** 400 boxes **Productivity Calculation:** \[ \text{Productivity} = \frac{\text{Total Boxes Produced}}{\text{Total Hours Worked}} \] \[ \text{Productivity} = \frac{400 \text{ boxes}}{40 \text{ hours}} = 10 \text{ boxes/hour} \] This confirms the initial productivity of **10 boxes/hour**. ### **After Redesign:** - **Desired Total Boxes Produced per Day:** 500 boxes - **Total Hours Worked per Day:** Remains **40 hours** **New Productivity Calculation:** \[ \text{New Productivity} = \frac{\text{Desired Total Boxes Produced}}{\text{Total Hours Worked}} \] \[ \text{New Productivity} = \frac{500 \text{ boxes}}{40 \text{ hours}} = 12.5 \text{ boxes/hour} \] Rounding to two decimal places, the new productivity is **12.50 boxes/hour**. --- **Answer to part b:** \(\boxed{12.50}\) boxes/hour