Divide 15 into two parts such that product of square of one part and cube of other is maximum

Explanation

Let numbers be `x` and `y`

Given , `x+y=15`

Now, `z=x^2y^3`

`implies z=x^2(15-x)^3`

`implies {dz}/{dx}=2x(15-x)^3-3x^2(15-x)^2`

For maximum value of `z`, `{dz}/{dx}=0`

`implies 2x(15-x)^3-3x^2(15-x)^2=0`

`implies 30x-2x^2=3x^2`

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