Question:easy
Consider an assembly line producing an item through a process involving three activities in the following order: cutting, welding, and polishing. There are three workers available: one is assigned only for cutting, one is assigned only for welding, and one is assigned only for polishing.
The activity time per item is given in the table.
Activity name Cutting Welding Polishing Activity time/item (in minutes) 30 40 25
Assuming that the process is running in steady state, the total number of items coming out of the assembly line in six hours is ______ (in integer).
Note: Assume that workers, items, and machines/tools are available as and when needed.
Consider an assembly line producing an item through a process involving three activities in the following order: cutting, welding, and polishing. There are three workers available: one is assigned only for cutting, one is assigned only for welding, and one is assigned only for polishing.
The activity time per item is given in the table.
Assuming that the process is running in steady state, the total number of items coming out of the assembly line in six hours is ______ (in integer).
Note: Assume that workers, items, and machines/tools are available as and when needed.
The activity time per item is given in the table.
| Activity name | Cutting | Welding | Polishing |
|---|---|---|---|
| Activity time/item (in minutes) | 30 | 40 | 25 |
Assuming that the process is running in steady state, the total number of items coming out of the assembly line in six hours is ______ (in integer).
Note: Assume that workers, items, and machines/tools are available as and when needed.
Show Hint
The slowest activity (largest time per item) sets the pace of the whole assembly line.
Updated On: Aug 5, 2026
Show Solution
Correct Answer: 9
Solution and Explanation
Step 1: Understanding the Concept:
We have a three-station sequential assembly line operating with dedicated workers. We need to determine the total production output over a 6 hour period running in a steady state.
Step 2: Key Formula or Approach:
In a sequential assembly line, the overall pace of production is entirely dictated by the slowest activity. This slowest step is known as the bottleneck.
The cycle time ($ C $) of the entire line equals the activity time of the bottleneck.
\[ \text{Throughput} = \frac{\text{Total Available Time}}{\text{Cycle Time}} \]
Step 3: Detailed Explanation:
Identify the bottleneck activity:
Cutting = 30 mins.
Welding = 40 mins.
Polishing = 25 mins.
The longest activity is Welding (40 minutes). Therefore, the cycle time of the entire assembly line is 40 minutes per item. This means in steady state, a completed item drops off the end of the line exactly every 40 minutes.
Calculate the total available time:
\[ 6 \text{ hours} = 6 \times 60 = 360 \text{ minutes} \]
Calculate total production:
\[ \text{Total Items} = \frac{360 \text{ minutes}}{40 \text{ minutes/item}} = 9 \text{ items} \]
Final Answer:
The total number of items coming out of the assembly line is 9. The phrase "running in steady state" means you do not need to account for the initial transient fill up time of the empty assembly line, you simply divide the total time by the bottleneck time. \[ \boxed{9 \text{ items}} \]
We have a three-station sequential assembly line operating with dedicated workers. We need to determine the total production output over a 6 hour period running in a steady state.
Step 2: Key Formula or Approach:
In a sequential assembly line, the overall pace of production is entirely dictated by the slowest activity. This slowest step is known as the bottleneck.
The cycle time ($ C $) of the entire line equals the activity time of the bottleneck.
\[ \text{Throughput} = \frac{\text{Total Available Time}}{\text{Cycle Time}} \]
Step 3: Detailed Explanation:
Identify the bottleneck activity:
Cutting = 30 mins.
Welding = 40 mins.
Polishing = 25 mins.
The longest activity is Welding (40 minutes). Therefore, the cycle time of the entire assembly line is 40 minutes per item. This means in steady state, a completed item drops off the end of the line exactly every 40 minutes.
Calculate the total available time:
\[ 6 \text{ hours} = 6 \times 60 = 360 \text{ minutes} \]
Calculate total production:
\[ \text{Total Items} = \frac{360 \text{ minutes}}{40 \text{ minutes/item}} = 9 \text{ items} \]
Final Answer:
The total number of items coming out of the assembly line is 9. The phrase "running in steady state" means you do not need to account for the initial transient fill up time of the empty assembly line, you simply divide the total time by the bottleneck time. \[ \boxed{9 \text{ items}} \]
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