document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=82410>Question 82410</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A home-based company produces both hand-knitted scarves and sweaters.  The scarves take 2 hours of labor to produce, and the sweaters take 14 hours.  The labor available is limited to 40 hours per week, and the total production capacity is 5 items per week.  Write a system of inequalities representing this situation, where x is the number of scarves and y is the number of sweaters.  Then graph the system of inequalities. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #59014 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=59014\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A home-based company produces both hand-knitted scarves and sweaters.  <BR>\n" );
document.write( "The scarves take 2 hours of labor to produce, and the sweaters take 14 hours.<BR>\n" );
document.write( "The labor available is limited to 40 hours per week,<BR>\n" );
document.write( "Labor Inequality: 2x+14y<=40<BR>\n" );
document.write( "--------- <BR>\n" );
document.write( "and the total production capacity is 5 items per week<BR>\n" );
document.write( "Production Inequality: <BR>\n" );
document.write( "0<=x<=5<BR>\n" );
document.write( "0<=y<=5<BR>\n" );
document.write( "x+y<=5<BR>\n" );
document.write( "---------------.  <BR>\n" );
document.write( "Write a system of inequalities representing this situation, where x is the number of scarves and y is the number of sweaters.  <BR>\n" );
document.write( "----------<BR>\n" );
document.write( "Solve each inequality for y to get:<BR>\n" );
document.write( "y <= (-1/7)x+(20/7)<BR>\n" );
document.write( "y<=-x+5<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "Then graph the system of inequalities<BR>\n" );
document.write( "I can only graph the boundaries: You will have to determine<BR>\n" );
document.write( "the respective half-plane solution areas:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-1%2C10%2C-1%2C10%2C%28-1%2F7%29x%2B%2820%2F7%29%2C-x%2B5%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-1%2C10%2C-1%2C10%2C%28-1%2F7%29x%2B%2820%2F7%29%2C-x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );