Mechanical Engineering Exam > Mechanical Engineering Questions > Process X has fixed cost of Rs. 40,000 and va...
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Process X has fixed cost of Rs. 40,000 and variable cost of Rs. 9 per unit whereas process Y has fixed cost of Rs.16, 000 and variable cost of Rs. 24 per unit. At what production quantity, the total cost of X and Yare equal?
- a)1200 units
- b)1600 units
- c)2000 units
- d)2400 units
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Process X has fixed cost of Rs. 40,000 and variable cost of Rs. 9 per ...
Total cost of X = Total cost of Y or Fx + Q.Vx = Fy + Q.Vy
Most Upvoted Answer
Process X has fixed cost of Rs. 40,000 and variable cost of Rs. 9 per ...
Analysis:
To find the production quantity at which the total cost of processes X and Y are equal, we need to equate the total costs of both processes and solve for the production quantity.
Process X:
- Fixed cost = Rs. 40,000
- Variable cost = Rs. 9 per unit
Process Y:
- Fixed cost = Rs. 16,000
- Variable cost = Rs. 24 per unit
Let's assume the production quantity as 'Q' units.
Total cost of process X:
Total cost of process X = Fixed cost of X + Variable cost of X
Total cost of process X = Rs. 40,000 + (Rs. 9 × Q)
Total cost of process Y:
Total cost of process Y = Fixed cost of Y + Variable cost of Y
Total cost of process Y = Rs. 16,000 + (Rs. 24 × Q)
Equating the total costs:
Total cost of process X = Total cost of process Y
Rs. 40,000 + (Rs. 9 × Q) = Rs. 16,000 + (Rs. 24 × Q)
Solving the equation:
Rs. 40,000 - Rs. 16,000 = (Rs. 24 × Q) - (Rs. 9 × Q)
Rs. 24,000 = Rs. 15 × Q
Q = Rs. 24,000 / Rs. 15
Q = 1600 units
Therefore, the production quantity at which the total cost of processes X and Y are equal is 1600 units.
Conclusion:
The correct answer is option b) 1600 units.
To find the production quantity at which the total cost of processes X and Y are equal, we need to equate the total costs of both processes and solve for the production quantity.
Process X:
- Fixed cost = Rs. 40,000
- Variable cost = Rs. 9 per unit
Process Y:
- Fixed cost = Rs. 16,000
- Variable cost = Rs. 24 per unit
Let's assume the production quantity as 'Q' units.
Total cost of process X:
Total cost of process X = Fixed cost of X + Variable cost of X
Total cost of process X = Rs. 40,000 + (Rs. 9 × Q)
Total cost of process Y:
Total cost of process Y = Fixed cost of Y + Variable cost of Y
Total cost of process Y = Rs. 16,000 + (Rs. 24 × Q)
Equating the total costs:
Total cost of process X = Total cost of process Y
Rs. 40,000 + (Rs. 9 × Q) = Rs. 16,000 + (Rs. 24 × Q)
Solving the equation:
Rs. 40,000 - Rs. 16,000 = (Rs. 24 × Q) - (Rs. 9 × Q)
Rs. 24,000 = Rs. 15 × Q
Q = Rs. 24,000 / Rs. 15
Q = 1600 units
Therefore, the production quantity at which the total cost of processes X and Y are equal is 1600 units.
Conclusion:
The correct answer is option b) 1600 units.
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Process X has fixed cost of Rs. 40,000 and variable cost of Rs. 9 per unit whereas process Y has fixed cost of Rs.16, 000 and variable cost of Rs. 24 per unit. At what production quantity, the total cost of X and Yare equal?a)1200 units b)1600 units c)2000 units d)2400 unitsCorrect answer is option 'B'. Can you explain this answer?
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