GATE 2011 CS (CS1) – Question 8

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

Variable manufacturing cost is V=4q and fixed cost is F=100/q. How many units q minimize total V+F?

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Correct answer: (A) 5

Explanation

Minimize C(q)=4q+100/q for positive q. Its derivative is 4−100/q², zero at q=5; second derivative 200/q³ is positive. Thus five units, A. Alternatively AM–GM gives minimum 40 at equality 4q=100/q.

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