GATE | GATE CS 2011 | Question 63

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 minimize the total cost (V+F)?
(A) 5
(B) 4
(C) 7
(D) 6

Answer: (A)

Explanation: The value of V+F is 4q + 100/q = (4q2 + 100)/q
First derivative of the resultant equation will be (8q2 – (4q2 + 100)) / q2
For V+F to be minimum its first derivative must be equal to zero.
[(8q2 – (4q2 + 100)) / q2] = 0
4q2 – 100 = 0
4q2 = 100
q = 5.

For q = 5 the above equation will give minimum value.

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