Let's break down the problem step-by-step, understanding the logic behind each calculation and how to approach the workstation balancing. --- ## **Part A: Calculating the Minimum Number of Workstations** ### 1. **Understanding the given data:** - **Total task time per unit (T):** 60 minutes - **Units required per day (D):** 240 units - **Available production time per day (A):** 480 minutes - **Number of workstations (N):** To be determined --- ### 2. **Calculate Cycle Time (C):** The cycle time is the maximum amount of time allowed per workstation to meet production goals. \[ C = \frac{\text{Available production time per day}}{\text{Units required per day}} = \frac{A}{D} \] Plugging in the numbers: \[ C = \frac{480\, \text{minutes}}{240\, \text{units}} = 2\, \text{minutes} \] **Interpretation:** Each workstation should process a unit in no more than **2 minutes** to meet the daily demand. --- ### 3. **Determine the minimum number of workstations (N):** Using the formula: \[ N = \frac{\text{Total task time}}{\text{Cycle time}} \] Total task time for one unit is 60 minutes, but since multiple units are produced simultaneously, the total task time for all tasks (assuming all tasks are performed once per unit) is: \[ \text{Total task time} = \text{Number of tasks} \times \text{Time per task} \] However, in this context, the **Total task time** refers to the sum of task times across all tasks necessary for one unit, which is **60 minutes** (given). Thus: \[ N = \frac{60\, \text{minutes}}{2\, \text{minutes}} = 30 \] --- ### **Answer for Part A:** **The minimum number of workstations required is 30.** --- ## **Part B: Drawing and Explaining the Workstation Arrangement** ### 1. **Key points for the diagram:** - **Horizontal axis:** 30 workstations labeled from 1 to 30. - **Cycle time (C):** 2 minutes (indicating each workstation should process one or more tasks totaling 2 minutes). - **Task times per station:** Sum of task times assigned to each station should be as close to 2 minutes as possible, with none exceeding it. - **No idle time:** The total task time across all stations equals total available time, meaning full utilization with no idle time. --- ### 2. **Visual Representation:** While I cannot draw here, I can describe what the diagram should include: - **A horizontal line** with 30 equally spaced stations labeled from 1 to 30. - **Assignment of tasks:** Tasks are grouped and assigned to each station so that the sum of task times in each station is approximately 2 minutes. - **Cycle time marker:** A vertical line or label marking 2 minutes across the diagram. - **No idle time:** The total sum of task times assigned across all stations matches exactly 60 minutes, which is the total task time for one unit, ensuring maximum efficiency. --- ### 3. **Explanation of the arrangement:** - **Task grouping:** Tasks are partitioned into 30 groups, each totaling about 2 minutes. - **Flow:** Parts move sequentially from station 1 to station 30, with each station completing its assigned tasks within 2 minutes. - **Efficiency:** Because the sum of task times exactly matches the total cycle time times the number of stations, there is no idle time, and the line is balanced optimally. --- ## **Summary:** - **Minimum workstations needed:** **30** - **Cycle time:** **2 minutes** - **Workstation assignment:** Tasks grouped so each station's total task time ≈ 2 minutes, with no idle time. --- ## **Key Takeaways for Problem Solving:** - Use the cycle time formula to determine the maximum processing time per station. - Divide total task time by cycle time to find the minimum number of stations. - Assign tasks to stations carefully to ensure each station's total task time is as close as possible to the cycle time without exceeding it. - Visual diagrams help in understanding task grouping and flow, ensuring efficient line balancing. --- If you'd like, I can help you with an example of task grouping or a more detailed step-by-step of assigning specific tasks to each station.