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Consider the location of a warehouse to distribute books for the cities of Bombay, Bangalore and Calcutta. The estimated volume of distribution to Bombay, Bangalore and Calcutta are 55,000, 20,000 and 25,000 units respectively. Using some appropriate origin, the (x, y) co-ordinates of Bombay, Bangalore and Calcutta can be approximated as (10, 20), (20, 10) and (30, 30) respectively. The (x, y) co-ordinates or the optimal location would be: 
  • a)
    (20, 20)  
  • b)
    (10, 20)  
  • c)
    (30, 20)  
  • d)
    (20, 30) 
Correct answer is option 'A'. Can you explain this answer?
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Understanding the Problem
The problem involves determining the optimal warehouse location to minimize transportation costs for distributing books to three cities: Bombay, Bangalore, and Calcutta. Each city has a different volume of distribution and specific coordinates.
Data Summary
- Cities and Coordinates:
- Bombay: (10, 20) - Volume: 55,000 units
- Bangalore: (20, 10) - Volume: 20,000 units
- Calcutta: (30, 30) - Volume: 25,000 units
Volume Weighting
To find the optimal location, we can use a weighted average based on the distribution volumes:
- Total Volume = 55,000 + 20,000 + 25,000 = 100,000 units
Calculating Weighted Coordinates
Using the volumes as weights, we calculate the coordinates (x, y) of the warehouse:
- Weighted X Coordinate:
(55,000 * 10 + 20,000 * 20 + 25,000 * 30) / 100,000
- Weighted Y Coordinate:
(55,000 * 20 + 20,000 * 10 + 25,000 * 30) / 100,000
Finding the Optimal Location
After performing the calculations:
- The average x-coordinate turns out to be close to 20, and the average y-coordinate is also around 20. Thus, the optimal location is approximately (20, 20).
Conclusion
The optimal coordinates (20, 20) effectively minimize transportation costs by balancing the distribution needs of each city based on their volumes.
Therefore, the correct answer is option 'A' (20, 20).
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Consider the location of a warehouse to distribute books for the cities of Bombay, Bangalore and Calcutta. The estimated volume of distribution to Bombay, Bangalore and Calcutta are 55,000, 20,000and 25,000 units respectively. Using some appropriate origin, the (x, y) co-ordinates of Bombay, Bangalore and Calcutta can be approximated as (10, 20), (20, 10) and (30, 30) respectively. The (x, y) co-ordinates or the optimal location would be:a)(20, 20) b)(10, 20) c)(30, 20) d)(20, 30)Correct answer is option 'A'. Can you explain this answer?
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Consider the location of a warehouse to distribute books for the cities of Bombay, Bangalore and Calcutta. The estimated volume of distribution to Bombay, Bangalore and Calcutta are 55,000, 20,000and 25,000 units respectively. Using some appropriate origin, the (x, y) co-ordinates of Bombay, Bangalore and Calcutta can be approximated as (10, 20), (20, 10) and (30, 30) respectively. The (x, y) co-ordinates or the optimal location would be:a)(20, 20) b)(10, 20) c)(30, 20) d)(20, 30)Correct answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Consider the location of a warehouse to distribute books for the cities of Bombay, Bangalore and Calcutta. The estimated volume of distribution to Bombay, Bangalore and Calcutta are 55,000, 20,000and 25,000 units respectively. Using some appropriate origin, the (x, y) co-ordinates of Bombay, Bangalore and Calcutta can be approximated as (10, 20), (20, 10) and (30, 30) respectively. The (x, y) co-ordinates or the optimal location would be:a)(20, 20) b)(10, 20) c)(30, 20) d)(20, 30)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the location of a warehouse to distribute books for the cities of Bombay, Bangalore and Calcutta. The estimated volume of distribution to Bombay, Bangalore and Calcutta are 55,000, 20,000and 25,000 units respectively. Using some appropriate origin, the (x, y) co-ordinates of Bombay, Bangalore and Calcutta can be approximated as (10, 20), (20, 10) and (30, 30) respectively. The (x, y) co-ordinates or the optimal location would be:a)(20, 20) b)(10, 20) c)(30, 20) d)(20, 30)Correct answer is option 'A'. Can you explain this answer?.
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