document.write( "Question 534302: Find 2 positive real numbers whose product is the maximum given that the sum is twice the first and three times the second is 48 \n" ); document.write( "

Algebra.Com's Answer #351672 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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Find 2 positive real numbers whose product is the maximum given that the sum is twice the first and three times the second is 48
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\n" ); document.write( "Two numbers, x & y
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\n" ); document.write( "2x + 3y = 48
\n" ); document.write( "3y = -2x + 48
\n" ); document.write( "y = $\"-2%2F3\"$ x + 16
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\n" ); document.write( "x*y
\n" ); document.write( "replace y with ( $\"-2%2F3\"$ x+16)
\n" ); document.write( "write an equation
\n" ); document.write( "f(x) = x( $\"-2%2F3\"$ x+16)
\n" ); document.write( "f(x) = ( $\"-2%2F3\"$ x^2+16x)
\n" ); document.write( "find the axis of symmetry, x = -b/(2a)
\n" ); document.write( "x = $\"%28-16%29%2F%282%2A%28-2%2F3%29%29\"$
\n" ); document.write( "x = $\"%28-16%29%2F%28-4%2F3%29\"$
\n" ); document.write( "x = -16 * $\"-3%2F4\"$
\n" ); document.write( "x = +12 gives max on the above equation
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\n" ); document.write( "Find y
\n" ); document.write( "2(12) + 3y = 48
\n" ); document.write( "3y = 48-24
\n" ); document.write( "y = 24/3
\n" ); document.write( "y = 8
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\n" ); document.write( "The two real numbers for max xy: 12,8
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