Labor Efficiency in Tailoring: Understanding Man-Hours and Their Impact
Efficiency calculations in the garment industry are crucial for manufacturers looking to optimize production processes, reduce costs, and increase productivity. One common scenario involves determining the number of shirts that can be produced under different working conditions by varying the number of tailors and the number of working hours. This article will explore a specific example and provide a step-by-step guide on how to solve such problems using the concepts of man-hours.
Introduction
In the tailoring industry, it is often useful to calculate the number of garments (in this case, shirts) that can be produced based on the available labor. This calculation helps in understanding the impact of variations in the number of tailors and working hours on overall productivity.
The Given Scenario
The problem at hand is to find out how many shirts can be stitched by 10 tailors working 11 hours a day, given that 15 tailors working 8 hours a day can stitch 60 shirts. To solve this problem, we will use the concept of man-hours, which is a standardized unit of labor input.
Step-by-Step Solution
Step 1: Calculate the total man-hours of the original scenario
We start by calculating the total man-hours used by the original 15 tailors:
15 tailors working 8 hours a day:
Total man-hours 15 tailors times 8 hours 120 man-hours
In that time, they can stitch 60 shirts:
Shirts per man-hour 60 shirts / 120 man-hours 0.5 shirts per man-hour
This calculation shows that each man-hour is equivalent to producing 0.5 shirts.
Step 2: Calculate the total man-hours for the new scenario
Next, we calculate the total man-hours for 10 tailors working 11 hours a day:
10 tailors working 11 hours a day:
Total man-hours 10 tailors times 11 hours 110 man-hours
Step 3: Calculate the number of shirts that can be produced in the new scenario
Using the rate of 0.5 shirts per man-hour, we can now calculate the total number of shirts that can be stitched:
Total shirts 110 man-hours times 0.5 shirts per man-hour 55 shirts
Therefore, 10 tailors working 11 hours a day can stitch 55 shirts.
Alternative Methods and Verifications
Three alternative methods to solve this problem include:
Method 1: Using Tailor-Hours
Instead of calculating man-hours, we can use a direct calculation based on tailor-hours:
15 tailor - 60 Shirts1 Tailor - 60/15 4 Shirts8 hour - 60 shirts1 hour - 60/8 7.5 shirtsATQ1 Tailor - 4 Shirts10 Tailor - 40 shirts1 hour - 7.5 Shirts11 hour - 82.5 shirtsExact 83 shirts
This method uses the rate of shirts produced per tailor-hour to verify the solution.
Method 2: Consumed Man-Hours
We can also calculate the consumed man-hours and then find the corresponding shirt production:
158 120 tailor-hours1011 110 tailor-hours120 - 60110 - XX 110 * 60 / 120 55 shirtsThey can make 55 shirts
This method calculates the difference in man-hours and directly applies it to find the number of shirts produced.
Method 3: Rate of Production
Another method involves finding the constant rate of production and then applying it to the new conditions:
INITIAL CONDITIONS158 60 researcher-hours120 60 researcher-hours2 researcher-hours per shirt or it takes 2 tailor hours to make 1 PROBLEMnow we plug it in with our second set of conditions:1011 s2110 2s55 sThey can make 55 shirts
Conclusion
This example demonstrates the importance of understanding man-hours in tailoring and how varying the number of tailors and working hours can impact overall productivity. By using the concept of man-hours, we can accurately predict the number of shirts that can be produced under different conditions, ensuring efficient resource allocation and optimal production planning.