A Farmer Has Wants To Fence An Area Of 1.5 Million

Anonymous

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A farmer has wants to fence an area of 1.5 million square feet in arectangular field and then divide it in half with a fence parallelto one of the sides if the rectangle. How can he do this so as tominimize the cost of the fence?

 

Answer No.1

Anonymous

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The trick here is to set this up as an equation so you canminimize it. . The first step in approaching a problem like this is toidentify what you don't know. What you don't know are thelength and width of the rectangle in question, or the length of thedividing fence (other than that it will be equal to either thelength or the width of the rectangle). That gives youthree unknowns, which is probably more than you want to workwith. For now, let's call l the length and w the width. And let's go ahead and say that the width, w, will be the shorterof the two, so we know that the dividing fence will be thatlong. . What else do you know? You know that lw=1.5, so l =1.5/w. . What is it that you're trying to minimize? You're tryingto minimize the cost of the fence. Presumably that means wewant to minimize the total length of fencing involved. So weneed an equation for that total length, which we'll call L. . L = 2l + 3w . . . That should be enough to get you started. Remember,the trick here is to think systematically about your unknowns andyour knowns, and how to translate them into an equation you canwork with.

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