Question 1058410
Let {{{ L }}} = the length of the rectangle
Let {{{ W }}} = the width of the rectangle
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Use formula for perimeter of a rectangle
{{{ 2L + 2W = 60 }}} 
{{{ 2L = 60 - 2W }}}
{{{ L = 30 - W }}}
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Let {{{ A }}} = the area of the rectangle
{{{ A = W*L }}}
{{{ A = W*( 30 - W ) }}}
{{{ A = -W^2 + 30W }}}
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This is a parabola. To find the peak, use the
formula {{{ W[max] = -b/(2a) }}}, where the
form is:
{{{ A = a*W^2 + b*W + c }}} ( {{{ c=0 }}} )
{{{ W[max] = -30/(2*(-1) ) }}}
{{{ W[max] = 15 }}}
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Plug this result back into equation
{{{ A[max] = -15^2 + 30*15 }}}
{{{ A[max] = -225 + 450 }}}
{{{ A[max] = 225 }}} ft2
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{{{ A = W*L }}}
{{{ 225 = 15*L }}}
{{{ L = 15 }}} ft
The maximum area is a 15 x 15 square
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{{{ P(x)  = R(x) - C(x) }}}
{{{ P(x) = 1300x -x^2 - 3100 - 20x }}}
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{{{ P(x) = -x^2 + 1280x - 3100 }}}
This is the expression for profit
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Use formula for {{{ x[max] }}}
{{{ x[max] = -b/(2a) }}}
{{{ a = -1 }}}
{{{ b = 1280 }}}
{{{ x[max] = -1280/(2(-1)) }}}
{{{ x[max] = 640 }}}
Plug this value back into equation
{{{ P[max] = -640^2 + 1280*640 - 3100 }}}
{{{ P[max] = -409600 + 819200 - 3100 }}}
{{{ P[max] = 406500 }}} 
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Here's the plot of the profit:
{{{ graph( 600, 400, -160, 1600, -45000, 450000, -x^2 + 1280x - 3100 ) }}} 
My numbers look close