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Verified Answer :

johnkellock

3, 9

Product maximum 12
Sum = 3 + (3 x 9) = 30

Answer:

15, 15

Step-by-step explanation:

Let the first and second number be x and y.

Three times the second number = 3y

As sum of the first number and three times the second number is 30,

x + 3y =30

we get, x = 30 - 3y

We need to find  two positive real numbers whose product is  maximum.

Let P =xy = y(30-3y)=\(30y-3y^2\)

0n differentiating P with respect to y, we get

\(P'=30-6y\)

On putting \(P'=0\), we get \(30-6y=0\Rightarrow 6y=30\Rightarrow y=5\)

0n differentiating P ' with respect to y, we get

\(P''=-6\)

At y = 5, \(P''=-6< 0\)

So, y = 5 is a point of maxima.

At y = 5, \(x=30-3y=30-3(5)=30-15=15\)

So, the two positive numbers are 15, 15

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