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Maths-

General

Easy

Question

The maximum value of $x y$ when $x plus 2 y equals 8$ is

20
16
24
8

The correct answer is: 8

Given, $y equals fraction numerator 8 minus x over denominator 2 end fraction$
Let $p equals x y equals fraction numerator 8 x minus x to the power of 2 end exponent over denominator 2 end fraction$

$rightwards double arrow blank fraction numerator d p over denominator d x end fraction equals fraction numerator 1 over denominator 2 end fraction open parentheses 8 minus 2 x close parentheses$

For maxima or minima, put $fraction numerator d p over denominator d x end fraction equals 0$

$therefore blank 8 minus 2 x equals 0$

$rightwards double arrow blank x equals 4$

Again, $fraction numerator d to the power of 2 end exponent p over denominator d x to the power of 2 end exponent end fraction equals negative 1$

$rightwards double arrow blank open parentheses fraction numerator d to the power of 2 end exponent p over denominator d x to the power of 2 end exponent end fraction close parentheses equals negative 1 less than 0$

Thus, function is maximum at $x equals 4$ and $y equals 2$

Therefore, maximum value of $p equals 4 cross times 2 equals 8$

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