Question 863972
Let x be the left side and y be the bottom side.


Accounting for cost, {{{5x+1*y=80}}}.
Accounting for area, which you already did, {{{A=(xy)/2}}}.
Find A in terms of either variable x or y, and simplify.


{{{y=80-5x}}} from cost accounting.
{{{A=x(80-5x)/2}}}
{{{A=(80x-5x^2)/2}}}
{{{A=-(5/2)x^2+40x}}}
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Factoring this will make x intercepts easy to find, and the maximum A will be the midpoint of the x intercept value.
{{{A=x(40-(5/2)x)}}}
{{{highlight_green(x(40-(5/2)x)=0)}}}
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x=0 OR (5/2)x=40, x=80/5=16
{{{x=0}}} OR {{{x=16}}}
Maximum value of x is 8=x.
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According to the 80 dollar restriction, the maximum area occurs for {{{highlight(x=8)}}} and {{{highlight(y=80-5*8=40)}}}.
AREA QUANTITY : {{{8*40/2=highlight(160)}}} square feet.