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Find two positive numbers `x` and `y` such that their sum is 35 and the product `x^2\ y^5` is maximum.

Text Solution

Verified by Experts

Here, `x+y = 35`.
`:. x = 35-y`
Let `P = x^2y^5`
Then, `P = (35-y)^2(y)^5`
Now, for `P` to be maximum, `(dP)/(dy)` should be `0`.
`:. y^5(2(35-y))(-1) +(35-y)^2(5y^4) = 0`
`=>y^4(35-y)[-2y+5(35-y)] = 0`
`=>y^4(35-y)(175-7y) = 0`
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