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Maximum value of (x – 2y), subject to, xy <=10 is:

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carouselambra
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Maximum value of (x – 2y), subject to, xy <=10 is: [#permalink] New post   Updated on: 10 Sep 2021, 09:53
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Maximum value of (x – 2y), subject to, xy <=10 is:

(a) 5
(b) √10
(c) 10
(d) 20
(e) Infinity
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E

Originally posted by carouselambra on 10 Sep 2021, 09:11.
Last edited by Bunuel on 10 Sep 2021, 09:53, edited 2 times in total.
Renamed the topic.
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Re: Maximum value of (x – 2y), subject to, xy <=10 is: [#permalink] New post   10 Sep 2021, 10:28
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Asked: Maximum value of (x – 2y), subject to, xy <=10 is:

If x= 10; y -> - infinity
xy -> - infinity <=10
x - 2y -> infinity

IMO E
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Re: Maximum value of (x – 2y), subject to, xy <=10 is: [#permalink] New post   10 Sep 2021, 09:37
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carouselambra wrote:
Maximum value of (x – 2y), subject to, xy <=10 is:

(a) 5
(b) √10
(c) 10
(d) 20
(e) Infinity


To maximise x-2y, we have to maximise x and minimise y.

Now \(xy\leq 10\), and there is no restriction on x and y.

Thus, we can easily take x as \(10^{2000}\) and y as \(10^{-2000}\)

And answer to x-2y will be ~ \(10^{2000}\).

We can take infinite value for x.


E
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Re: Maximum value of (x – 2y), subject to, xy <=10 is: [#permalink] New post   10 Sep 2021, 09:56
carouselambra wrote:
Maximum value of (x – 2y), subject to, xy <=10 is:

(a) 5
(b) √10
(c) 10
(d) 20
(e) Infinity


let us take x=5 and y=-15 the equality is satisfied and we get the greatest definied value of 20

However proceeding in a similar fashion we can get any value that's positive by taking a large negatve and a corresponding x value

Therefore it can lead upto infinity therefore IMO E
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Re: Maximum value of (x – 2y), subject to, xy <=10 is: [#permalink] New post   21 Sep 2021, 06:48
(x-2y)^2=x^2+(4y)^2-4xy
For (x-2y) to be a maximum, (x-2y)^2 should also be a maximum and this would be possible if xy is minimum.Since there is no lower limit to the value of xy, it can be as infinitely negative as possible which would make x-2y infinitely positive.
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Re: Maximum value of (x – 2y), subject to, xy <=10 is: [#permalink]
21 Sep 2021, 06:48
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