if x + y = 50, what is the maximum value of the product of x and y that is possible?

Given: $x + y =50$

To find: Maximum value of $x \times y$

$x + y =50$

$y =50 - x$

Substitute in $x \times y$

= $x \times (50-x) $

= $50x -x^2 $

= $50x -x^2 $
 

If $a < 0$, quadratic expression has greatest value at $x = – \frac{b}{2a}$ 

Our quadratic expression has $a = -1$ and $b = 50$. So greatest value is at $x = – \frac{50}{-2}$ 

Greatest value is at $x =25$ 

Substitute $x =25$

We get

=$50 \times 25 -25^2 $

= $25(50-25)$

= $25(25)$

= 625

So maximum value is 625

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Updated on: 10-Oct-2022

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