#### Question

Find two positive numbers *x* and *y* such that *x* + *y* = 60 and *xy*^{3} is maximum.

#### Solution

The two numbers are *x* and *y* such that *x* + *y* = 60.

⇒ *y* = 60 − *x*

Let *f*(*x*) = *xy*^{3.}

^{}

∴By second derivative test, *x *= 15 is a point of local maxima of *f*. Thus, function *xy*^{3} is maximum when *x* = 15 and *y* = 60 − 15 = 45.

Hence, the required numbers are 15 and 45.

Is there an error in this question or solution?

Solution Find Two Positive Numbers X and Y Such that X + Y = 60 and Xy3 is Maximum. Concept: Maxima and Minima.