Question

If (x, y) lie in first quadrant on the line 3x + 4y = 5 then greatest value of $x^2.y^3$ is

• A. 5
• B. 7
• C. $\frac{1}{7}$
• D. $\frac{3}{16}$

Answer 1

The correct option is D $\frac{3}{16}$

Consider ${\left(\frac{3x}{2}\right)}^2{\left(\frac{4y}{3}\right)}^3$ the product of five factors whose sum is $2.\frac{3x}{2}+3.\frac{4y}{3}=5$
$\therefore$ Product will be Maximum when all factors one equal
$\therefore \frac{3x}{2}=\frac{4y}{3}=\frac{3x+4y}{2+3}=1\Rightarrow x=\frac{2}{3};y=\frac{3}{4}$
$\therefore x^2.y^3=\frac{3}{16}$