Let's carefully walk through each part of the problem step-by-step. --- ## **Part A: Calculate the minimum number of workstations required** ### **Step 1: Determine the cycle time (C)** The cycle time is the maximum amount of time each workstation has to complete its assigned tasks so that the production meets demand. **Formula:** \[ C = \frac{\text{Available production time per day}}{\text{Units required per day}} \] **Given data:** - Available time per day = 480 minutes - Units required per day = 240 units **Calculation:** \[ C = \frac{480 \text{ minutes}}{240 \text{ units}} = 2 \text{ minutes per unit} \] **Interpretation:** Each unit must be produced in 2 minutes to meet the daily demand. --- ### **Step 2: Calculate the minimum number of workstations (N)** **Formula:** \[ N = \frac{\text{Total task time}}{\text{Cycle time}} \] **Given data:** - Total task time per unit = 60 minutes - Cycle time (C) = 2 minutes **Calculation:** \[ N = \frac{60 \text{ minutes}}{2 \text{ minutes}} = 30 \] **Result:** **The minimum number of workstations needed is 30.** --- ## **Part B: Draw a labeled diagram to represent the workstation arrangement** ### **Step 1: Understand the setup** - Number of workstations: 30 - Total task time: 60 minutes - Cycle time: 2 minutes - No idle time in this configuration (aiming for perfect balance) ### **Step 2: Distribute tasks among workstations** Since total task time is 60 minutes and there are 30 workstations: \[ \text{Task time per workstation} = \frac{60 \text{ minutes}}{30} = 2 \text{ minutes} \] **This matches the cycle time, indicating a balanced line with no idle time.** ### **Step 3: Diagram description** - **Horizontal axis:** Label from 1 to 30, each representing a workstation. - **Vertical labels:** Show task time per station (each 2 minutes). - **Cycle time:** Indicate as 2 minutes at the top. - **Idle time:** Zero, since each workstation's task time equals the cycle time. --- ### **Step 4: Sketching the diagram** Here's a textual representation of the line: ``` Workstations: | 1 | 2 | 3 | ... | 30 | Task time per station: 2 min for each workstation Cycle Time: 2 minutes (indicated above the line) Total task time: 60 minutes (sum of all workstations) No idle time: Each workstation is fully utilized ``` --- ## **Final Answers:** ### **Part A:** **The minimum number of workstations required is:** \[ \boxed{30} \] --- ### **Part B:** **Diagram (conceptual):** ``` [Workstation 1] -- 2 min task [Workstation 2] -- 2 min task ... [Workstation 30] -- 2 min task Cycle Time = 2 minutes Total Task Time = 60 minutes No idle time in this configuration ``` *(In an actual drawing, you'd represent this line with 30 boxes labeled 1 to 30, each annotated with "2 min task" and a note indicating "Cycle Time = 2 min," with no gaps or idle segments.)* --- **Summary:** - **Minimum workstations needed:** **30** - **Balanced line with no idle time, each station completing 2 minutes of work, synchronized with the cycle time.**