This question seems strange to me. Can you please state the source?
Thanx!
Inequality(Maximum Value)
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goalevan
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The product of two numbers (a and b) under a sum constraint (a + b < x) is maximized when a = b.
But the sum of numbers under a product constraint is maximized when these numbers DO NOT equal each other. An extreme example is (1/10000)*(120000) = 12, for which the sum is greater than 120,000.
To solve, we can maximize one of the numbers and minimize the other, given the constraints.
a <= 5 and b <= 3, so we can set a = 5 and b = 12/5 = 2.4.
a + b is then 25/5 + 12/5 = 37/5, while satisfying the constraints ab = 12, a <= 5, and b <=3.
But the sum of numbers under a product constraint is maximized when these numbers DO NOT equal each other. An extreme example is (1/10000)*(120000) = 12, for which the sum is greater than 120,000.
To solve, we can maximize one of the numbers and minimize the other, given the constraints.
a <= 5 and b <= 3, so we can set a = 5 and b = 12/5 = 2.4.
a + b is then 25/5 + 12/5 = 37/5, while satisfying the constraints ab = 12, a <= 5, and b <=3.
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kevincanspain
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The two numbers are a and 12/a, where a is between 4 and 5 inclusivevishu1414 wrote:Hi
Please help me to approach the problem :
If a<=5 ,b <=3 ,and ab=12 ,What is maximum possible value of (a+b)?
A)23/5
B)34/5
C)7
D)37/5
E)9
Ans:D
The sum is a + 12/a , which increases as a increases from 4 to 5 (12/a decreases from 3 to 2.4, a change of only 0.6, not enough to offset the increase in a)
When a=5, a + 12/a = 5 + 12/5 = 37/5
Kevin Armstrong
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