document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=70495>Question 70495</A>: <I><SPAN STYLE=\"word-break: break-all;\"> well for class we have to read a word problem and define variables i dont know how to do this ..here is the problem\r<BR>\n" );
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document.write( "Wanda, Xavier, and yolanda have a small business producing handmade shawls and afghans for the Mathematics Teachers Retirement Home. They spin the yarn, dye the yarn, and weave the cloth. A shawl requires one hour of spinning, one hour of dyeing, and one hour of weaving. An afghan requires 2 hours of spinning one hour of dyeing and four hours of weaving. They make a profit of $16 per shawl and $20 per afghan. Xavier does the spinning on his day off when he can spend at most eight hours spinning. Yolanda does the dyeing on her day off when she can spend up to six hours dyeing. Wanda does all of the weaving on Friday and Saturday when she has at most fourteen hours available. The trio would like to maximize their profit. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #50373 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=50373\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let L = the number of shawLs made<BR>\n" );
document.write( "Let N = the number of afghaNs made<BR>\n" );
document.write( "The hours needed to make a shawl are<BR>\n" );
document.write( "(S-1, D-1, W-1) 3 hours total for Spinning, Dying, Weaving<BR>\n" );
document.write( "The hours needed to make an afghan are<BR>\n" );
document.write( "(S-2, D-1, W-4) 7 hours total for Spinning, Dying, Weaving<BR>\n" );
document.write( "For the spinning process,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+%2B+2N ALIGN=MIDDLE  ALT=\"L+%2B+2N\"   DISABLED_style= \"max-width:90%; height:auto;\" > represents the hours needed to make <BR>\n" );
document.write( "L shawLs and N afghaNs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+%2B+2N+%3C=+8 ALIGN=MIDDLE  ALT=\"L+%2B+2N+%3C=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > eight hours are available for spinning process<BR>\n" );
document.write( "when L shawLs and N afghaNs are made<BR>\n" );
document.write( "likewise,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+%2B+N+%3C=+6 ALIGN=MIDDLE  ALT=\"L+%2B+N+%3C=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > six hours are available for dying when L shawLs and N afghaNs are made<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+%2B+4N+%3C=+14 ALIGN=MIDDLE  ALT=\"L+%2B+4N+%3C=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" > fourteen hours are available for dying when L shawLs and N afghaNs are made<BR>\n" );
document.write( "I next graph L versus N for each equation and see what makes sense<BR>\n" );
document.write( "L is measured on the vertical axis, n on the horizontal<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-4%2C+10%2C+-4%2C+20%2C+8-2x%2C+6-x%2C+14-4x+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-4%2C+10%2C+-4%2C+20%2C+8-2x%2C+6-x%2C+14-4x+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "As I see from the graph, If N were > 3.5, the weaving process <BR>\n" );
document.write( "would not get done at all, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N+%3C+3.5 ALIGN=MIDDLE  ALT=\"N+%3C+3.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "As I see from the graph, If L were > 6, the dying process<BR>\n" );
document.write( "would not get done at all, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+%3C+6 ALIGN=MIDDLE  ALT=\"L+%3C+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The equation for profit is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16L+%2B+20N+=+P ALIGN=MIDDLE  ALT=\"16L+%2B+20N+=+P\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The range of possible L and N are in the area enclosed by the<BR>\n" );
document.write( "lines and the axes. An s,d,or w means not possible because there are<BR>\n" );
document.write( "not enough hours to complete one of the 3 processes. Otherwise,<BR>\n" );
document.write( "I note the profit.<BR>\n" );
document.write( "(N,L)<BR>\n" );
document.write( "(3,1)76.....(2,1)56....(1,1)36<BR>\n" );
document.write( "(3,2)92.....(2,2)72....(1,2)52<BR>\n" );
document.write( "(3,3)s,w....(2,3)88....(1,3)68<BR>\n" );
document.write( "(3,4)s,d,w..(2,4)104...(1,4)84<BR>\n" );
document.write( "(3,5)s,d,w..(2,5)s,d...(1,5)100<BR>\n" );
document.write( "The maximum profit of $104 occurs when 2 afghans and 4 shawls<BR>\n" );
document.write( "are made. Xavier spends <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%2B2N+=+8 ALIGN=MIDDLE  ALT=\"L%2B2N+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >hours spinning. Yolande<BR>\n" );
document.write( "spends <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%2BN+=+6 ALIGN=MIDDLE  ALT=\"L%2BN+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >hours dyeing. Wanda spends <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%2B4N+=+12 ALIGN=MIDDLE  ALT=\"L%2B4N+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "hours weaving.\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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