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GATE | GATE CS 2011 | Question 63

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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 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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Last Updated : 17 May, 2019
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