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The variable cost (V) of manufacturing a product varies according to the equation V = 4q, where q is the quantity produced. The fixed cost (F) of production of same product reduces with q according to the equation F = 100/q. How many units should be produced to minimise the total cost (V + F)?
- a)4
- b)7
- c)5
- d)6
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
The variable cost (V) of manufacturing a product varies according to t...
Understanding the Problem
Given:
Variable Cost (V) = 4q
Fixed Cost (F) = 100/q
To minimize the total cost (V + F), we need to find the quantity q that will result in the lowest total cost.
Calculating Total Cost
Total Cost (TC) = V + F
TC = 4q + 100/q
Finding the Minimum Total Cost
To find the minimum total cost, we need to differentiate TC with respect to q and set it to zero.
d(TC)/dq = 4 - 100/q^2
Setting the derivative to zero:
4 - 100/q^2 = 0
4q^2 = 100
q^2 = 25
q = 5
Therefore, to minimize the total cost, 5 units should be produced.
Conclusion
The correct answer is option C, 5 units should be produced to minimize the total cost.
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The variable cost (V) of manufacturing a product varies according to t...
To minimise the total cost (V + F), let f(q) = (V + F).
f(q) = 4q + 100/q
f'(q) = 4 - 100/q2
f'(q) = 0
Solving, q = 5, -5
Since q can not be negative, so q = 5 is the required answer to minimize total cost.
f(q) = 4q + 100/q
f'(q) = 4 - 100/q2
f'(q) = 0
Solving, q = 5, -5
Since q can not be negative, so q = 5 is the required answer to minimize total cost.
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The variable cost (V) of manufacturing a product varies according to the equation V = 4q, where q is the quantity produced. The fixed cost (F) of production of same product reduces with q according to the equation F = 100/q. How many units should be produced to minimise the total cost (V + F)?a)4b)7c)5d)6Correct answer is option 'C'. Can you explain this answer?
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