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hitmoss: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Mon May 04, 2009 11:38 am; Location: India

by hitmoss » Sun Sep 18, 2011 6:04 am

if 5x + 2y = 15 then find out the maximum value of (x^3)*(y^2)?

Hitmoss:)

"Dreams are not what you see in sleep, Dreams is the thing does not let you sleep."

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Source: Beat The GMAT — Problem Solving | Sun Sep 18, 2011 6:04 am

gmatclubmember: Master | Next Rank: 500 Posts; Posts: 158; Joined: Sat Sep 03, 2011 10:31 amFollowed by: 2 members; Thanked: 29 times

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.

Cheers
Ami/-

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hitmoss: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Mon May 04, 2009 11:38 am; Location: India

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?

Hitmoss:)

"Dreams are not what you see in sleep, Dreams is the thing does not let you sleep."

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Abhishek009: Master | Next Rank: 500 Posts; Posts: 359; Joined: Wed Mar 11, 2009 4:37 amFollowed by: 2 members; Location: Kolkata, India; Thanked: 50 times

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

Abhishek

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gmatclubmember: Master | Next Rank: 500 Posts; Posts: 158; Joined: Sat Sep 03, 2011 10:31 amFollowed by: 2 members; Thanked: 29 times

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.

Cheers
Ami/-

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