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Unformatted text preview: 4. least cost = $64 correct 5. least cost = $60 Explanation: Let x be the length of the side made of heavy duty material, and y the length of the adjacent sides. Then the cost of the fencing is given by C ( x,y ) = 6 x + 2( x + 2 y ) = 2(4 x + 2 y ) , while the area of the Feld is given by Area = xy = 32 . As a function solely of x , therefore, C ( x ) = 2 n 4 x + 64 x o . Dierentiating C ( x ) with respect to x we see that C ( x ) = 2 n 4-64 x 2 o . The critical point of C is thus the solution of C ( x ) = 2 n 4-64 x 2 o = 0 , i.e. , x = 4. Since C 00 ( x ) = 128 x 3 , C ( x ) will be minimized when x = 4 (which is the only critical point to make practical sense anyway!). Consequently, the pen has least cost = $64 , and this occurs when it is a 4 8 yard rectan-gle....
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- Spring '08