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October 12th, 2011, 05:08 PM  #1 
Newbie Joined: Sep 2011 Posts: 13 Thanks: 0  mathematical modeling
a farmer needs to build a rectangular pen next to his driveway. its area must be 600 square meters. the fence for the driveway side of the pen costs 5 dollars per meter, and the fence for the other three sides costs only 3 dollars per meter. find a function that models the cost of the fence in terms of the length of the driveway side in terms of the length of the driveway. is this right? 3(3x)+5y= cost xy=600 so x=600/y the would you plug this in for x? 
October 12th, 2011, 05:52 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: mathematical modeling
Letting y be the length of fence along the driveway, and x be the perpendicular length of the rectangle, we find the cost C in dollars: C = 5y + 3(2x + y) = 8y + 6x We know xy = 600, thus x = 600/y, then: C(y) = 8y+6(600/y) = 8(y + 450/y) You were on the right track, you just made the 3 $3/m sides equal to x in length, when 2 of them are x and 1 is y, the side opposite the one next to the driveway. Make a sketch and you will clearly see what I am talking about. 

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