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- anonymous

The sum of a number and twice another number is 12. What is their maximum product?

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- anonymous

The sum of a number and twice another number is 12. What is their maximum product?

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- anonymous

hello!!!
suppose the number be x so the other number will be 2x
so according to question
x + 2x = 12
3x = 12
x = 4
so 2x = 8
product = 8 * 4
= 32
this the simplest way to solve the problem but maybe its incorrect because of "maximum product".

- anonymous

ChatIndia, you cannot use x + 2x because that would imply they are the same number. It has to be x + 2y.
I'm still working on this answer :p

- anonymous

Yea because it says another number!

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- anonymous

nkili, in that case it would be very easy to solve. thanks for the hint

- anonymous

i am sleepy,nkili will solve the problem. :)

- anonymous

I'm really not sure about this one actually haha.... sorry :/

- anonymous

proceed this way (x +2y)^2 = 144

- anonymous

Does anyone disagree with 18?

- anonymous

My answer key says that's the right answer, but how do you solve it.

- anonymous

16

- anonymous

Let x y = k
y=k/x
Then
\[\frac{k}{x}+2 x==12 \]
\[\frac{k-12 x+2 x^2}{x}=0 \]
Derivative of the Numerator set to 0 then solved for x is
x=3
\[\left(\frac{k}{x}+2 x==12\text{/.}x\to 3\right) \text{is}\text{ }\left(6+\frac{k}{3}==12\right) \]
k=18

- anonymous

maxima minima trick :P

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