GATE 2012 CS (CS1) – Question 1

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

A firm’s cost is $5q^2$ for production q and its selling price is 50 per unit. How many units maximize profit?

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Correct answer: (A) 5

Explanation

Profit is $\pi(q)=50q-5q^2$. Its derivative 50−10q vanishes at q=5; the second derivative −10 is negative. Equivalently π=125−5(q−5)², so the maximum occurs at 5 units, A.

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