Question

Find two numbers whose sum is 15 and when the square of one multiplied by the cube of the other is maximum.

Answer 1

Let the two numbers be x and y. 

Then x + y = 15 

∴ y = 15 – x 

Let P is the product of square of y and cube of x.

In both cases, product x³y² is zero, which is not maximum.

∴ P is maximum when x = 6 

If x = 6, then y = 15 – 6 = 9 

Hence, the required numbers are 6 and 9.