document.write( "Question 511607: Find a pair of numbers with a sum of 26 and a product that is a maximum. Find the maximum product. \n" ); document.write( "

Algebra.Com's Answer #342294 by oberobic(2304) $\"\"$ $\"About$

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x + y = 26
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\n" ); document.write( "x = 26-y
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\n" ); document.write( "The product is
\n" ); document.write( "z = x * y = (26-y) * y
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\n" ); document.write( "z = 26y -y^2
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\n" ); document.write( "To find the maximum, take the first derivative and solve it.
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\n" ); document.write( "dz/dy = 26 - 2y
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\n" ); document.write( "26-2y = 0
\n" ); document.write( "26 = 2y
\n" ); document.write( "y = 13
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\n" ); document.write( "Check:
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y	x=26-y	x*y
13	13	169
12	14	168
11	15	165
10	16	160
9	17	153
8	18	144
7	19	133
6	20	120
5	21	105
4	22	88
3	23	69
2	24	48
1	25	25

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\n" ); document.write( "Answer: The pair of numbers are 13 and 13 that total 26 and maximizes the product.
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\n" ); document.write( "Done. \n" ); document.write( "

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