Let's tackle the problem step by step as requested: --- ## Step 1: Draw Precedence Diagram **Explanation:** A precedence diagram shows the order in which tasks must be performed, based on their dependencies. We use the table to connect each task to its predecessor(s). **Diagram:** ``` A / \ B C | / \ D E F \ / G ``` - **A** has no predecessor. - **B** depends on A. - **C** depends on A. - **D** depends on B. - **E** and **F** depend on C. - **G** depends on D, E, and F. --- ## Step 2: Calculate Cycle Time **Explanation:** Cycle time is the maximum time each workstation has to complete its assigned tasks to meet the required output. - **Total production time available** = 4 hours = 4 × 360 = 14,400 seconds - **Required output** = 120 chargers **Formula:** \[ \text{Cycle Time (CT)} = \frac{\text{Total Production Time}}{\text{Required Output}} \] \[ \text{CT} = \frac{14,400 \text{ sec}}{120} = 120 \text{ sec/charger} \] --- ### Final Answers for Steps 1 and 2 1. **Precedence Diagram:** (See above diagram) 2. **Cycle Time:** **120 seconds per charger** --- Let me know if you'd like to proceed to the next steps!

## Step 3: Find Theoretical Minimum Workstations **Explanation:** The theoretical minimum workstations (W) can be determined by dividing the total task time by the cycle time. ### Total Task Time Calculation - Task A: 15 sec - Task B: 10 sec - Task C: 12 sec - Task D: 20 sec - Task E: 14 sec - Task F: 8 sec - Task G: 18 sec **Total Task Time (T):** \[ T = 15 + 10 + 12 + 20 + 14 + 8 + 18 = 97 \text{ sec} \] ### Theoretical Minimum Workstations Formula \[ W = \frac{T}{CT} \] \[ W = \frac{97 \text{ sec}}{120 \text{ sec}} \approx 0.81 \] Since the number of workstations must be a whole number, we round up: \[ W = 1 \] --- ## Step 4: Assign Tasks to Workstations **Explanation:** We distribute the tasks to the available workstations based on their dependencies and the cycle time. ### Tasks Assignment: - **Workstation 1:** A (15 sec) + B (10 sec) + D (20 sec) **Total: 45 sec** (Under cycle time of 120 sec) Remaining tasks: - **C (12 sec)** - **E (14 sec)** - **F (8 sec)** - **G (18 sec)** - **Workstation 2:** C (12 sec) + E (14 sec) + F (8 sec) **Total: 34 sec** (Under cycle time of 120 sec) - **Workstation 3:** G (18 sec) **Total: 18 sec** (Under cycle time of 120 sec) **Total Workstations: 3** --- ## Step 5: Calculate Efficiency **Explanation:** Efficiency measures how effectively the workstations are utilized in relation to the available working time. ### Efficiency Formula \[ \text{Efficiency} = \frac{\text{Total Task Time}}{\text{Number of Workstations} \times \text{Cycle Time}} \times 100\% \] \[ \text{Efficiency} = \frac{97 \text{ sec}}{3 \times 120 \text{ sec}} \times 100\% \] \[ \text{Efficiency} = \frac{97}{360} \times 100\% \approx 26.94\% \] --- ### Final Answers for All Steps 1. **Precedence Diagram:** (See above diagram) 2. **Cycle Time:** **120 seconds per charger** 3. **Theoretical Minimum Workstations:** **1 workstation (rounded up)** 4. **Assigned Tasks to Workstations:** - Workstation 1: A, B, D - Workstation 2: C, E, F - Workstation 3: G 5. **Efficiency:** **Approximately 26.94%** Let me know if you need further assistance!