Question 361779
{{{A+B+C=60}}}
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.
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{{{B=4*A}}}
Substituting.
{{{A+4A+C=60}}}
1.{{{5A+C=60}}}
Then the product is,
{{{P=AC}}}
From eq. 1,
{{{C=60-5A}}}
Substitute,
{{{P=A(60-5A)}}}
{{{P=60A-5A^2}}}
To find the maximum, put the equation into vertex form by completing the square.
{{{P=-5A^2+60A}}}
{{{P=-5(A^2-12A)}}}
{{{P=-5(A^2-12A+36)+5(36)}}}
{{{P=-5(A-6)^2+180}}}
The maximum occurs when {{{highlight(A=6)}}} and has a value of {{{highlight(P[max]=180)}}}. 
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{{{B=4A}}}
{{{highlight(B=24)}}}
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{{{C=60-5(6)}}}
{{{highlight(C=30)}}}