document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73425>Question 73425</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having problems with this one.This is what I have so far.<BR>\n" );
document.write( "x=number of items produced<BR>\n" );
document.write( "C=cost in dollars <BR>\n" );
document.write( "100items=$10,000<BR>\n" );
document.write( "300items=$22,000<BR>\n" );
document.write( "Business and finance. In planning for a new item, a manufacturer assumes that<BR>\n" );
document.write( "the number of items produced x and the cost in dollars C of producing these items are related by a linear equation. Projections are that 100 items will cost $10,000 to produce and that 300 items will cost $22,000 to produce. Find the equation that relates C and x.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52564 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=52564\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since this is a linear equation by assumption, the slope-intercept form can be used.  This <BR>\n" );
document.write( "equation will be in the form y = mx + b.  But we will redefine the variables.  Replace<BR>\n" );
document.write( "y with C the cost. x will still be used to represent the number of items produced. x will be on<BR>\n" );
document.write( "the x-axis and C will be on the y-axis.<BR>\n" );
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document.write( "As the number of items manufactured increases from 100 to 300 units (an increase of 200 items)<BR>\n" );
document.write( "the cost goes from $10,000 to $22,000 (an increase of $12,000).  The slope of this graph is,<BR>\n" );
document.write( "therefore:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12000%2F200=+60 ALIGN=MIDDLE  ALT=\"12000%2F200=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "and the 60 represents the dollars that it costs to produce a unit.<BR>\n" );
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document.write( "So far our equation is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+60%2Ax+%2B+b ALIGN=MIDDLE  ALT=\"C+=+60%2Ax+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The question now is how do we calculate b? We can use the fact that when x = 100, then<BR>\n" );
document.write( "C = $10,000. Plug these values into the equation and you find:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10000+=+60%2A100+%2B+b+ ALIGN=MIDDLE  ALT=\"10000+=+60%2A100+%2B+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This simplifies to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10000+=+6000+%2B+b ALIGN=MIDDLE  ALT=\"10000+=+6000+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Subtract 6000 from both sides and you find that <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4000+=+b ALIGN=MIDDLE  ALT=\"4000+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Plug that value into the equation and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+60%2Ax+%2B+4000 ALIGN=MIDDLE  ALT=\"C+=+60%2Ax+%2B+4000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This is the equation that relates C and x (thenCost and number of items produced).  <BR>\n" );
document.write( "Notice something interesting.  If you produced no items (x = 0) the cost is still $4000.  <BR>\n" );
document.write( "This probably involves the cost of labor to maintain the assembly line, store the materials, <BR>\n" );
document.write( "keep the lights and heat on, and so forth.  <BR>\n" );
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document.write( "Hope this helps you to understand the graphing process.  You can check the equation out<BR>\n" );
document.write( "by letting x = 300 items and see if the cost computes to $22,000 as specified in the problem. </SPAN>\n" );
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