Optimization Problem: Express 18 as a sum of two positive numbers...

[xnyaan]

The problem is: Express 18 as a sum of two positive numbers whose product of the first and square of the second is as large as possible.

So far I know that 0 < x < 18
x+y=18
y=18-x

and i know their maybe a y^2.

what i don't understand is what they mean by product of the first? do they mean the first number as in 2x or do they mean x*y^2 or am i completely off?
what equation would be formed? y=x(18-x)?

thank you!

 

[Deleted member 4993]

The problem is: Express 18 as a sum of two positive numbers whose product of the first and square of the second is as large as possible.

So far I know that 0 < x < 18
x+y=18
y=18-x

and i know their maybe a y^2.

what i don't understand is what they mean by product of the first? do they mean the first number as in 2x or do they mean x*y^2 or am i completely off?
what equation would be formed? y=x(18-x)?

thank you!

As I see it, you need to maximize:

M = x * y^2 = (18-y) * y^2

Now calculate y for maximum M and then calculate x.