document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=110452>Question 110452</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.	Matrix methods can be used to solve linear programming problems. A linear programming problem is used to find an optimal solution, subject to stated restraints. <BR>\n" );
document.write( "One typical application is to maximize profits. For example, a beauty parlor provides both highlighting and permanent wave services. It costs $5 in materials and requires 30 minutes to provide highlighting. However, it costs $12 in materials but requires 80 minutes to provide a perm. The store has at most $120 in materials and 800 minutes in labor per day to expend. <BR>\n" );
document.write( "How many highlighting services and how many perms can the beauty parlor perform daily to maximize cost and time?<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 #80508 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=80508\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> One typical application is to maximize profits. For example, a beauty parlor provides both highlighting and permanent wave services. <BR>\n" );
document.write( "It costs $5 in materials and requires 30 minutes to provide highlighting. <BR>\n" );
document.write( "It costs $12 in materials but requires 80 minutes to provide a perm. <BR>\n" );
document.write( "The store has at most $120 in materials and 800 minutes in labor per day to expend. <BR>\n" );
document.write( "How many highlighting services and how many perms can the beauty parlor perform daily to maximize cost and time?<BR>\n" );
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document.write( "Let \"h\" be # of highlighting jobs ; Let \"P\" be # of perm jobs.<BR>\n" );
document.write( "h>=0<BR>\n" );
document.write( "p>=0<BR>\n" );
document.write( "Materials Inequality : 5h  + 12m <= 120<BR>\n" );
document.write( "Time Inequality      : 30h + 80m <= 800<BR>\n" );
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document.write( "Graph these equations on a h/m coordinate system.<BR>\n" );
document.write( "h <= (-12/5)m+24<BR>\n" );
document.write( "h <= (-8/3)m + 80/3<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C50%2C-10%2C50%2C%28-12%2F5%29x%2B24%2C%28-8%2F3%29x%2B%2880%2F3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Find the vertices of the solution space:<BR>\n" );
document.write( "(0,0), (0,24), (0,10)<BR>\n" );
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document.write( "Determine Profit at these vertex values: <BR>\n" );
document.write( "(0,0) implies 0 profit<BR>\n" );
document.write( "(0,24) implies 12*24 = $288 profit<BR>\n" );
document.write( "(0,10 implies 12*10 = $120 profit<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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