Maximum value of (x – 2y), subject to, xy

Question

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

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

chetan2u · Answer

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

Crytiocanalyst · Answer

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

Kinshook · Answer

Asked: Maximum value of (x – 2y), subject to, xy <=10 is: If x= 10; y -> - infinity xy -> - infinity <=10 x - 2y -> infinity IMO E

Isa1989 · Answer

(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.

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

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

Prep Toolkit

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