Question

The maximum value of \(x^2 y z^3\), subject to \(x + y + z = 42\) exist at \((x, y, z) = (\alpha, \beta, \gamma)\), then \(\alpha\beta\gamma =\)

• A. \(6 \times 7^3\)
• B. \(7 \times 6^3\)
• C. \(14 \times 7 \times 21\)
• D. \(12 \times 6 \times 24\)

Hint:

For maximizing \(x^a y^b z^c\) given \(x+y+z=S\), directly write \(x = \frac{a}{a+b+c}S\), \(y = \frac{b}{a+b+c}S\), and \(z = \frac{c}{a+b+c}S\).
This saves valuable time spent writing out the long AM-GM inequalities.

Answer 1

The Correct Option is A