document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=886052>Question 886052</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Minimum Cost: A rectangular area adjacent to a river is to be fenced in; no fence is needed on the river side. The enclosed area is to be 1,000 square feet. Fencing for the side parallel to the river is $5 per linear foot, and fencing for the other two sides is $8 per linear foot; the four corner posts are $25 apiece. Let x be the length of one of the sides perpendicular to the river. <BR>\n" );
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document.write( "a)      Write a function C(x) that describes the cost of the project.<BR>\n" );
document.write( "b)      What is the domain of C?\r<BR>\n" );
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document.write( " I don't know exactly how to do this. Any suggestions on what I mess up on is greatly appreciated. \r<BR>\n" );
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document.write( " 4 * 25 = 100 NOT A VARIABLE COST\r<BR>\n" );
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document.write( " 5y * 8x = 1,000       I put it like this because it is a rectangle and I was trying to get the area. So I multiplied l * w. \r<BR>\n" );
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document.write( "5y * 8x - 5y = 1,000 - 5y<BR>\n" );
document.write( "8x = -5y + 1,000<BR>\n" );
document.write( "8x - 1,000 = -5y + 1,000 - 1,000<BR>\n" );
document.write( "8x - 1,000 = -5y<BR>\n" );
document.write( "8x - 1,000 / -5 = -5y / -5<BR>\n" );
document.write( "-8/5x - 200 <BR>\n" );
document.write( "C(x) = - 8/5x - 200\r<BR>\n" );
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document.write( "I was told it was wrong. I've also tried the following. \r<BR>\n" );
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document.write( "8x^2 + 5 y + 100 = 1000<BR>\n" );
document.write( "8x^2 5y + 100 - 100 = 1000 - 100<BR>\n" );
document.write( "8x^2 + 5y = 900<BR>\n" );
document.write( "8x^2 + 5y - 8x^2 = -8x^2 + 900<BR>\n" );
document.write( "5y = -8x^2 + 900<BR>\n" );
document.write( "5y / 5 = -8x2 + 900 / 5<BR>\n" );
document.write( "y = -8/5x^2 +180\r<BR>\n" );
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document.write( "8x + 8x + 5y + 100 = 1000<BR>\n" );
document.write( "16x + 5y + 100 = 1000<BR>\n" );
document.write( "16x + 5y + 100 - 100 = 1000 - 100 <BR>\n" );
document.write( "16x + 5y = 900<BR>\n" );
document.write( "16x + 5y - 16x = -16x + 900<BR>\n" );
document.write( "5y = -16x + 900<BR>\n" );
document.write( "5y / 5 = -16x + 900 / 5<BR>\n" );
document.write( "y = -16/5x + 180\r<BR>\n" );
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document.write( "I'm not sure how to explain the cost of the project or to find the domain either. \r<BR>\n" );
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document.write( "Thank you in advance. Chastity Moore </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #535654 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=535654\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x represents the length of the side perpendicular to the river.<BR>\n" );
document.write( "let y represent the length of the side parallel to the river.<BR>\n" );
document.write( "the perimeter is equal to 2x + y<BR>\n" );
document.write( "since the cost per foot of x is equal to 8, then the cost of x feet is equal to 8 * x.<BR>\n" );
document.write( "since the cost per foot of y is equal to 5, then the cost of y feet is equal to 5 * y.<BR>\n" );
document.write( "the cost of the perimeter of fencing is equal to (4 * 25) + (2 * 8 * x) + (5 * y)<BR>\n" );
document.write( "the 4 * 25 is the cost of the 4 posts.<BR>\n" );
document.write( "the 2 * 8 * x is the cost of the sides perpendicular to the river.<BR>\n" );
document.write( "the 5 * y is the cost of the side parallel to the river.\r<BR>\n" );
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document.write( "since the area is equal to length * width and x is the width and y is the length, then the area is equal x * y<BR>\n" );
document.write( "since the area is equal to 1000 square feet, then you get:<BR>\n" );
document.write( "x * y = 1000<BR>\n" );
document.write( "if you solve for y, you get y = 1000 / x.\r<BR>\n" );
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document.write( "substitute for y in the cost equation and you get:<BR>\n" );
document.write( "c(x) = (4 * 25) + (2 * 8 * x) + (5 * (1000 / x))\r<BR>\n" );
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document.write( "simplify this equation to get:<BR>\n" );
document.write( "c(x) = 100 + (16 * x) + (5000 / x).\r<BR>\n" );
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document.write( "the value of x cannot be less than or equal to 0.<BR>\n" );
document.write( "the value of x has to be less than infinity.<BR>\n" );
document.write( "the value of y will be based on the equation of y = 1000 / x, because the area will always have to be 1000 and the equation for the area is x * y = 1000 and when you solve for y in the equation of x * y = 1000, you get y = 1000 / x.\r<BR>\n" );
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document.write( "if you graph this equation, you will find that the minimum cost for the perimeter is when x = 17.677671.<BR>\n" );
document.write( "When x = 17.677671, y = 1000 / 17.677671 = 56.56853779<BR>\n" );
document.write( "finding this value is not very easy.<BR>\n" );
document.write( "I used the TI-84 plus graphing calculator to find it for me.\r<BR>\n" );
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document.write( "when x = 17.677671 and y = 56.56853779, the cost for the fencing becomes 615.6854249.\r<BR>\n" );
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document.write( "you can see from the graph shown below, that this is the minimum cost for the perimeter.\r<BR>\n" );
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document.write( "the domain of the function of c(x) = 100 + (16 * x) + (5000 / x) is equal to all values of x greater than 0.\r<BR>\n" );
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document.write( "the range of the function of c(x) is equal to all values of y greater than or equal to 615.6854249.\r<BR>\n" );
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document.write( "you can see both of those from the graph as well.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/jul0704.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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