Sure! Let's go through this step-by-step to understand how to determine the number of workstations needed for the assembly line and visualize the workstation arrangement. --- ### **Step 1: Understand the given data** - **Total task time per unit**: 60 minutes - **Daily demand (units needed)**: 240 units - **Available production time per day**: 480 minutes --- ### **Step 2: Calculate the Cycle Time (C)** **Cycle Time (C)** is the maximum amount of time each workstation has to produce one unit, ensuring the total demand is met within the available time. The formula: \[ C = \frac{\text{Available production time per day}}{\text{Units required per day}} \] Plug in the values: \[ C = \frac{480 \text{ minutes}}{240 \text{ units}} = 2 \text{ minutes} \] **Interpretation**: Each workstation must complete its assigned tasks in **2 minutes** to meet daily demand. --- ### **Step 3: Calculate 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 given as 60 minutes, but since the line is balancing multiple units simultaneously, the total task time for the entire line during production is: \[ \text{Total task time} = \text{Number of units} \times \text{Task time per unit} = 240 \times 60 \] But **this approach isn't necessary** if we consider the **total task time** per unit (which is 60 minutes). Instead, for line balancing, we look at: \[ N = \frac{\text{Sum of task times of all tasks}}{\text{Cycle time}} \] Since the **total task time per unit is 60 minutes**, and the **cycle time is 2 minutes**, the **minimum number of workstations**: \[ N = \frac{60 \text{ minutes}}{2 \text{ minutes}} = 30 \] **Final answer for part A**: \[ \boxed{ \textbf{A) Minimum number of workstations} = 30 } \] --- ### **Step 4: Draw a labeled diagram of workstation arrangement** **Key points for the diagram**: - There are **30 workstations** arranged linearly along the production line. - Each workstation is assigned a set of tasks such that the total task time per station is **equal to the cycle time** (2 minutes). - The **total task time per station** is designed so **no idle time** exists (100% utilization). --- ### **Step 5: Determine task assignment per workstation** Since total task time per unit is 60 minutes, and we are dividing tasks evenly across 30 stations: \[ \text{Task time per station} = \frac{60 \text{ minutes}}{30} = 2 \text{ minutes} \] This matches the cycle time, so **each station's total task time = 2 minutes**. --- ### **Step 6: Visualize the line (conceptual diagram)** Here's how you can visualize it: ``` Line Diagram (Horizontal axis: Workstations 1 to 30) ---------------------------------------------------------- | W1 | W2 | W3 | W4 | ... | W29 | W30 | ---------------------------------------------------------- - Each workstation (W1 to W30) performs tasks totaling 2 minutes. - The total cycle time is 2 minutes. - Since total task time (60 min) divided by 30 stations = 2 min per station, there's no idle time. ``` **Additional notes:** - **Task assignment**: Tasks are divided among stations such that no station exceeds 2 minutes. - **No idle time**: Because task times exactly match cycle time, each station is fully occupied. --- ### **Summary** | Part | Calculation / Explanation | Final Answer | |--------|------------------------------|--------------| | **A)** | Minimum number of workstations | **30** | | **B)** | Diagram showing 30 stations, each with 2 min task time, cycle time marked as 2 min, and no idle time | *Visualized above* | --- ### **Final notes** - This line balancing ensures smooth flow with minimal idle time. - Real-world scenarios may require slight adjustments for task dependencies, but this provides the ideal theoretical setup. --- If you'd like, I can help you sketch a detailed diagram or explore how to assign specific tasks to each station!