Question 1140031
<pre>

L*W = 122                   (1)

Cost equation:
C = 20L + 10L + 10W + 10W   
C = 30L + 20W               (2)  

Eq (1) -->   L = 122/W

Substitute for L in (2):

C = 30*(122/W) + 20W
C = 3660/W + 20W

Differentiate WRT to W:
dC/dW = -(3660/W^2) + 20

Set the derivative to 0:
  -(3660/W^2) + 20 = 0
   20W^2 = 3660
     W^2 = 183
     W  = {{{ highlight( 13.52775 ) }}} ft

L = 122/13.52775 = {{{highlight(9.01850) }}} ft


[ min(C) = $541.11   for these dimensions ]

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