document.write( "Question 1078617: A box manufacturer is to produce a closed box of volume 4500 cubic inches, where the base is a rectangle having length three times its width. What are the dimensions of the box constructed with the least amount of material?\r
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Algebra.Com's Answer #693060 by ikleyn(52776)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Bottom or top dimensions, \r\n" );
document.write( "length 3w, width w\r\n" );
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document.write( "h, for height\r\n" );
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document.write( "Given volume 4500,\r\n" );
document.write( "\"3w%2Aw%2Ah=4500\"\r\n" );
document.write( "\"3w%5E2h=4500\"\r\n" );
document.write( "\"h%2Aw%5E2=1500\"     (1)\r\n" );
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document.write( "Total surface area\r\n" );
document.write( "S = \"3w%5E2%2B3w%5E2%2B3wh%2B3wh%2Bwh%2Bwh\" = \"6w%5E2%2B8wh\"    (2)\r\n" );
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document.write( "From (1), express h = \"1500%2Fw%5E2\" and substitute it into (2). You will get\r\n" );
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document.write( "S = \"highlight_green%286w%5E2%2B12000%2Fw%29\"\r\n" );
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document.write( "  \"%28d%2Fdw%29%286w%5E2%2B12000%2Fw%29\" = \r\n" );
document.write( "= \"12w%2B12000%28-1%29w%5E%28-2%29\"\r\n" );
document.write( "= \"%2812w%5E3-12000%29%2Fw%5E2\"\r\n" );
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document.write( "\"d%2Fdw+=+0\"\r\n" );
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document.write( "\"12w%5E3-12000=0\"\r\n" );
document.write( "\"w%5E3-1000=0\"\r\n" );
document.write( "\"w%5E3=1000=10%5E3\"\r\n" );
document.write( "\"highlight_green%28w=10%29\", width\r\n" );
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document.write( "Length, 3w\r\n" );
document.write( "\"highlight_green%2830%29\"\r\n" );
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