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Inequalities

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Inequalities

by hitmoss » Sun Sep 18, 2011 6:04 am
if 5x + 2y = 15 then find out the maximum value of (x^3)*(y^2)?
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by gmatclubmember » Sun Sep 18, 2011 6:37 am
hitmoss wrote:if 5x + 2y = 15 then find out the maximum value of (x^3)*(y^2)?
Is this qs complete? Is there any condition missing like x,y are +ve integers or something ?
Well I got the answer using differentiation but not an elegant way (though it took me under 2 mins), but still I think the question is incomplete. Could you please confirm?
Well I got the max value at x=9/5,y=3 which is 6561/125.

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by hitmoss » Sun Sep 18, 2011 7:32 am
x,y are positive integers.

can you please explain how did you got the figures x=9/5 and y=3?
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by Abhishek009 » Sun Sep 18, 2011 7:37 am
hitmoss wrote:if 5x + 2y = 15 then find out the maximum value of (x^3)*(y^2)?
Assuming X and Y are both Integers...

Lets maximize either X or Y


Possible conditions :

X = 1 ; Y = 5 So (x^3)*(y^2) = (1^3)(5^2) => 25

X = 3 ; Y = 0 So (x^3)*(y^2) = (3^3)(0^3)=> 0



So we can say the maximum value is X = 1 ; Y = 5
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by gmatclubmember » Sun Sep 18, 2011 7:39 am
Hello hitmoss,
Forget about my earlier solution because that was solved without the consideration of positive integers. That used differentiation and GMAT wont expect us to solve any qs with differentiation.
But if you still need to know the methodology please PM me.

Now coming to question and a new condition that the x,y are +ve integers:
5x+2y =15 is possible only when x=1 and y=5.
So max(x^3*y^2) = 25.

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