Question 273266: from all the pairs of numbers whose sum is 256, find the pair whose product is greatest. Found 2 solutions by stanbon, CharlesG2:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! from all the pairs of numbers whose sum is 256, find the pair whose product is greatest.
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x + y = 256
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Product = xy = x(256-x) = 256x-x^2
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P(x) = -x^2+256x
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Max occurs when x = -b/2a = -256/(-2) = 128
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If x = 128, y = 128
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Cheers,
Stan H.
You can put this solution on YOUR website! from all the pairs of numbers whose sum is 256, find the pair whose product is greatest.
pair of numbers: a and b
a + b = 256
a * b greatest = ?
this will be when a and b are both greatest or a=128 and b=128,
then a*b = 128 * 128 = 16384
this is similar to when you have a set perimeter for a rectangle, a square will always have the greatest area
following table is proof:
a b a*b
0 256 0
1 255 255
2 254 508
...
125 131 16375
126 130 16380
127 129 16383
128 128 16384
129 127 16383
130 126 16380
131 125 16375
132 124 16368
133 123 16359
134 122 16348
135 121 16335
...
254 2 508
255 1 255
256 0 0
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