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Fundamental Principle of Counting

If the sum of...

Question

If the sum of two +ve numbers is 18, then the maximum value of their product is

A

81

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B

85

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C

72

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D

80

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Solution

The correct option is D 81
$x + y = 18$
$P r o d u c t = x y$
$\frac{d (P r o d u c t)}{d x} = (18 - x) - x$
$0 = 18 - 2 x$
$x = 9$
$y = 9$
$P r o d u c t = 81$

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