Lesson20_-_Optimization_ws-sol

Lesson20_-_Optimization_ws-sol - Solutions to Worksheet for...

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Solutions to Worksheet for Section 4.5 Optimization Problems V63.0121, Calculus I Spring 2010 1. An advertisement consists of a rectangular printed region plus 1 in margins on the sides and 2 in margins on the top and bottom. If the area of the printed region is to be 92 in 2 , find the dimensions of the printed region and overall advertisement that minimize the total area. Solution. The objective is to minimize the total area while the printed area is fixed. Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu 2 cm 2 cm 1 cm x y Let the dimensions of the printed region be x and y ; then the printed area is P = xy 92 while the total area is A = ( x + 2)( y + 4). From the P equation we can isolate y = 92 /x and substitute it into the A equation to get A ( x ) = ( x + 2) ± 92 x + 4 ² FOIL = 92 + 4 x + 184 x + 8 = 100 + 4 x + 184 x 1
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The domain of A is (0 , ).
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This note was uploaded on 07/19/2010 for the course MATHEMATIC V63.0121 taught by Professor Leingang during the Spring '09 term at NYU.

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Lesson20_-_Optimization_ws-sol - Solutions to Worksheet for...

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