Allied & ICAR Exam Bank • ALLIED_2654 NAT • 2 Marks

Section 1: Engineering Mathematics

Calculus

Subtopic: Maxima and minima of function with several independent variables

Question Statement:

The maximum value of $f(x, y) = x y$ subject to the constraint $x + y = 10$ with $x, y > 0$ is:

Answer Key:

25

Step-by-Step Solution & Explanation

Substitute $y = 10 - x \implies f(x) = x(10 - x) = 10x - x^2$. Maximum occurs at $x = 5$, giving $f(5, 5) = 25$.
← Previous (ALLIED_2653) Next (ALLIED_2655) →

Practice In Authentic CBT Exam Interface

Test your skills under authentic timed conditions with live scoring and AIR percentile ranking.

Launch CBT Mock Test