document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=60372>Question 60372</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780073268620/algebrahomeworkh>Elementry and Intermediate Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Hello,\r<BR>\n" );
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document.write( "Do I need to rearange this type problem to solve?\r<BR>\n" );
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document.write( "Please advise....\r<BR>\n" );
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document.write( "Thanks.\r<BR>\n" );
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document.write( "Q 19: A company uses the cost function C (w) = 0.04 w^2 – 6.0 w + 275 to model the unit cost in dollars for producing ‘w’ widgets. Find:\r<BR>\n" );
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document.write( "a.	How many widgets the company needs to make to achieve minimum unit cost?<BR>\n" );
document.write( "b.	What is the minimum unit cost?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #41472 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=41472\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can plot this equation or just picture what it should look like<BR>\n" );
document.write( "I'll just try to describe it.<BR>\n" );
document.write( "(1) Because the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2 ALIGN=MIDDLE  ALT=\"w%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > term is positive, the graph is a parabola<BR>\n" );
document.write( "that slopes negatively down from the left, comes down to a minimum and<BR>\n" );
document.write( "slopes back up positively.<BR>\n" );
document.write( "(2) The problem is to find the minimum. The minimum will be half way<BR>\n" );
document.write( "between two values of w that have the same C(w), in other words, half<BR>\n" );
document.write( "way between the points (w[1],C[1]) and (w[2],C[2]) where C[1] = C[2]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+.04%2Aw%5E2+-+6%2Aw+%2B+275 ALIGN=MIDDLE  ALT=\"C+=+.04%2Aw%5E2+-+6%2Aw+%2B+275\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If they don't produce any widgets, the fixed cost is $275<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+.04%2A0+-+6%2A0+%2B+275 ALIGN=MIDDLE  ALT=\"C+=+.04%2A0+-+6%2A0+%2B+275\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+275 ALIGN=MIDDLE  ALT=\"C+=+275\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now, if I find another value of w for which C(w) = 275, the C(w) mid-<BR>\n" );
document.write( "way between (0,275) and (w[2],275) will be minimum cost<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+.04%2Aw%5E2+%96+6%2Aw+%2B+275 ALIGN=MIDDLE  ALT=\"C+=+.04%2Aw%5E2+%96+6%2Aw+%2B+275\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=275+=+.04%2Aw%5E2+%96+6%2Aw+%2B+275 ALIGN=MIDDLE  ALT=\"275+=+.04%2Aw%5E2+%96+6%2Aw+%2B+275\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "subtract 275 from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.04%2Aw%5E2+%96+6%2Aw+=+0 ALIGN=MIDDLE  ALT=\".04%2Aw%5E2+%96+6%2Aw+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%2A%28.04%2Aw+-+6%29+=+0 ALIGN=MIDDLE  ALT=\"w%2A%28.04%2Aw+-+6%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If the 1st factor, w, is zero, that's the point we already have, (0,275)<BR>\n" );
document.write( "so, set the 2nd factor equal to zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.04%2Aw+-+6+=+0 ALIGN=MIDDLE  ALT=\".04%2Aw+-+6+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.04%2Aw+=+6 ALIGN=MIDDLE  ALT=\".04%2Aw+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+150 ALIGN=MIDDLE  ALT=\"w+=+150\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That's our 2nd point. We now have (0,275 and (150,275)<BR>\n" );
document.write( "The minimum C is halfway between the w's, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150%2F2+=+75 ALIGN=MIDDLE  ALT=\"150%2F2+=+75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That's the answer to (a), 75 widgets made give minimum cost<BR>\n" );
document.write( "Now find C(w)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+.04%2Aw%5E2+-+6%2Aw+%2B+275 ALIGN=MIDDLE  ALT=\"C+=+.04%2Aw%5E2+-+6%2Aw+%2B+275\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+.04%2A%2875%29%5E2+-+6%2A%2875%29+%2B+275 ALIGN=MIDDLE  ALT=\"C+=+.04%2A%2875%29%5E2+-+6%2A%2875%29+%2B+275\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+.04%2A5625+-+450+%2B+275 ALIGN=MIDDLE  ALT=\"C+=+.04%2A5625+-+450+%2B+275\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+225+-+450+%2B+275 ALIGN=MIDDLE  ALT=\"C+=+225+-+450+%2B+275\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+50 ALIGN=MIDDLE  ALT=\"C+=+50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That means the min is at (75,50) and the answer to (b) is<BR>\n" );
document.write( "the minimum unit cost is $50<BR>\n" );
document.write( "A simple test will tell you if this is truly the min<BR>\n" );
document.write( "Find C(w) for w = 74.9 and for w= 75.1. These values of w should <BR>\n" );
document.write( "give costs that are both slightly higher than $50.<BR>\n" );
document.write( "I get C(w) = 50.0004 for both   </SPAN>\n" );
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