Question

The sum of two +ve numbers is 100. If the product of the square of one number and the cube of the other is maximum then the numbers are

• A. 60, 40
• B. 20, 80
• C. 80, 20
• D. 40, 60

Answer 1

The correct option is D 40, 60

$x+y=100$
$f\left(x\right)=x^2(100-x{)}^3$
$f^{\prime }\left(x\right)=2x(100-x{)}^3-3(100-x{)}^2{x}^2$
$3x=2(100-x)$
$x=40$ $y=60$