document.write( "Question 66207: an open top box is to be made so that its width is 4 ft and its volume is 40 ft^3. the base of the box costs $4/ft^2and the sides cost $2/ft^2.
\n" ); document.write( "A) express the cost of the box as a function of its length (l) and height (h).
\n" ); document.write( "B) find a relationship between (l) and (h)
\n" ); document.write( "C) express the cost as a function of (h) only
\n" ); document.write( "D) give the domain of the cost function
\n" ); document.write( "E) using a graphing calculator or ocmputer to approximate the dimensions of the box having the least cost. \n" ); document.write( "
Algebra.Com's Answer #46963 by ankor@dixie-net.com(22740)\"\" \"About 
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an open top box is to be made so that its width is 4 ft and its volume is 40 ft^3. the base of the box costs $4/ft^2and the sides cost $2/ft^2.
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\n" ); document.write( "A) express the cost of the box as a function of its length (L) and height (h).
\n" ); document.write( ":
\n" ); document.write( "Cost = base cost + 4 sides cost (2 of one size and 2 of another size)
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\n" ); document.write( "Cost = $4(4*L) + 2[$2(4*h)] + 2[$2(L*h)]
\n" ); document.write( "Cost = 16L + 16h + 4L*h
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\n" ); document.write( "B) find a relationship between (L) and (h)
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\n" ); document.write( "Using the vol equation:
\n" ); document.write( "L*w*h = 40
\n" ); document.write( "L*4*h = 40
\n" ); document.write( "4L*h =40
\n" ); document.write( "L*h = 40/4
\n" ); document.write( "L*h = 10
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\n" ); document.write( "L = 10/h
\n" ); document.write( "and
\n" ); document.write( "h = 10/L
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\n" ); document.write( "C) express the cost as a function of (h) only
\n" ); document.write( ":
\n" ); document.write( "Using the cost equation: Cost = 16L + 16h + 4L*h, substitute (10/h) for L:
\n" ); document.write( "Cost = 16(10/h) + 16h + 4[(10/h)*h)
\n" ); document.write( "Cost = (160/h) + 16h + 40; note that the h's cancel
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\n" ); document.write( "D) give the domain of the cost function
\n" ); document.write( "(0,+infinity)
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\n" ); document.write( "E) using a graphing calculator or computer to approximate the dimensions of the box having the least cost.
\n" ); document.write( "Enter:
\n" ); document.write( " y = (160/x) + 16x + 40; x represents the height and y represents the cost.
\n" ); document.write( "Using the minimum feature I got x = 3.162, (height); y = 141.19, (min cost)
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\n" ); document.write( "It's interesting to note that the min cost occurs when both the height and the
\n" ); document.write( "length = 3.162, so two of the sides are square. (L = 10/3.162 = 3.162)
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\n" ); document.write( "Dimensions of the box: 3.162 x 4 x 3.162 = 39.9929, (close enough to 40 cu ft)
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\n" ); document.write( "Hope this helped you, it doesn't seem the the domain could increase forever
\n" ); document.write( "and practically it couldn't, but no algebra reason for it not to?? Ask your
\n" ); document.write( "instructor about that. \n" ); document.write( "
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