Kingsly, here you would have to say since we want y^3, let’s split 12y as 4y + 4y + 4y. So we need x = 4y so 4y * y^3 = 64 so y = 2 and x = 8 and so x + 12y = 32 I would guess…
There won’t be a maximum limit, Abhishek. If we make a and b very small (close to zero), then c will become very large (tending to infinity) and so the total will tend to infinity as well. Remember that we are talking positive real numbers here and not integers.
If 2x+y =8, maximum value of x^4 * y^3, Solved it by taking 2x/4 =y/3 which implies, taking value of x =2 and y =3 so maximum is 2^4 * 3^3 but answer is given to be as 2^18 * 3^3. the answer was explained in A.M>= G.M approach. could you please explain the flaw in my logic.
Neither answer seems correct. If we don’t have a condition on x and y, then it can go to infinity. If we restrict x and y to be positive, even then the max will come when x = 16/7 and y = 24/7. You have assumed x and y to be natural numbers I guess, but I see no reason for that in the question.
Do double-check the question; the answer 2^18*3^3 would come if the question was 2x+y = 28. Perhaps you have read it incorrectly or else there is a typo in the question….
I saw a question on quora. Find max value of 3x + 4y=12.
I got the right answer when I tried with 3x/2 + 3x/2 + 4y/2+4y/2=12 however my answer is wrong when I tried putting 3x/3 + 3x/3 + 3x/3 + 4y/2 + 4y/2 =12. Why is it so? Need help.
Sorry sir. The question is “Is it possible to find the maximum value of 3x+4y=12? “.It’s clear from your comment that it is not.Can you tell me the reason?
That still doesn’t make sense. A valid question could be something like “Find the maximum value of x^2 + y^2 given that 3x + 4y = 12”. Or “Find the maximum value of 3x + 4y given that x^2 + y^2 = 12”.
This question is like asking “find the maximum value of x = 4”. There is nothing to find here as everything is fixed already. Possibly the person who posted it was in a hurry and missed out something.
CAT-holics 
xy^3 = 64.
find minimum value of x+12y.
i tried the method as above, i get x= 4th root of (64/27)….pls advice
Kingsly, here you would have to say since we want y^3, let’s split 12y as 4y + 4y + 4y. So we need x = 4y so 4y * y^3 = 64 so y = 2 and x = 8 and so x + 12y = 32 I would guess…
regards
J
Hi J,
Shouldn’t it be x, 4y/3 + 4y/3 + 4y/3. Hence,
x = 4y/3 ?
No Dev, the sum needs to be 12y
For the last problem, what will be the maximum value of a+b+c when a^2*b*c^4 = 1024. Please explain ?
There won’t be a maximum limit, Abhishek. If we make a and b very small (close to zero), then c will become very large (tending to infinity) and so the total will tend to infinity as well. Remember that we are talking positive real numbers here and not integers.
regards
J
It was helpful. Thank you
If 2x+y =8, maximum value of x^4 * y^3, Solved it by taking 2x/4 =y/3 which implies, taking value of x =2 and y =3 so maximum is 2^4 * 3^3 but answer is given to be as 2^18 * 3^3. the answer was explained in A.M>= G.M approach. could you please explain the flaw in my logic.
Neither answer seems correct. If we don’t have a condition on x and y, then it can go to infinity. If we restrict x and y to be positive, even then the max will come when x = 16/7 and y = 24/7. You have assumed x and y to be natural numbers I guess, but I see no reason for that in the question.
Do double-check the question; the answer 2^18*3^3 would come if the question was 2x+y = 28. Perhaps you have read it incorrectly or else there is a typo in the question….
regards
J
I saw a question on quora. Find max value of 3x + 4y=12.
I got the right answer when I tried with 3x/2 + 3x/2 + 4y/2+4y/2=12 however my answer is wrong when I tried putting 3x/3 + 3x/3 + 3x/3 + 4y/2 + 4y/2 =12. Why is it so? Need help.
“Find max value of 3x + 4y=12” is an incomplete question. (That value will always be 12!) If you provide the complete question, maybe I can help.
regards
J
Sorry sir. The question is “Is it possible to find the maximum value of 3x+4y=12? “.It’s clear from your comment that it is not.Can you tell me the reason?
That still doesn’t make sense. A valid question could be something like “Find the maximum value of x^2 + y^2 given that 3x + 4y = 12”. Or “Find the maximum value of 3x + 4y given that x^2 + y^2 = 12”.
This question is like asking “find the maximum value of x = 4”. There is nothing to find here as everything is fixed already. Possibly the person who posted it was in a hurry and missed out something.
regards
J