SOLUTION: Find two numbers whose sum is 28 and whose product is the maximum possible value. What two numbers yield this​ product?

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Question 1138954: Find two numbers whose sum is
28 and whose product is the maximum possible value.
What two numbers yield this​ product?

Found 2 solutions by josmiceli, rothauserc:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let one of the number be +x+
+f%28x%29+=+x%2A%28+28+-++x+%29
+f%28x%29+=+-x%5E2+%2B+28x+
+x%5Bmax%5D+=+-28%2F%282%2A%28-1%29%29+
+x%5Bmax%5D+=+14+
and
+28+-+x+=+14+
Both numbers are 14
check:
Here's the plot:
+graph%28+400%2C+400%2C+-20%2C+30%2C+-20%2C+200%2C+-x%5E2+%2B+28x+%29+

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
let x, y be the two numbers
:
x + y = 28
:
if the two numbers are 1 and 27, then
:
1) x + y = 28
:
2) xy = 27
:
solve equation 1 for y, then substitute for y in equation 2
:
3) y = 28 -x
:
x(28-x) = 27
:
4) -x^2 +28x -27 = 0
:
the graph of equation 4 is a parabola that curves downward, so the coordinates of the vertex is the maximum values for x and y
:
x coordinate = -b/2a = -28/2(-1) = 14
:
substitute for x in equation 3
:
y = 28 -14 = 14
:
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the maximum product occurs when x=14 and y=14
:
Note 14 * 14 = 196
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