document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=162545>Question 162545</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Slip and Slide Ski Company manufactures downhill skis and cross country skis. A pair of downhill skis requires 2 man-hours for cutting, 1 man-hour for shaping, and 3 man-hours for finishing while a pair of cross country skis requires 2 man-hours for cutting, 2 man-hours for shaping, and 1 man-hour for finishing. Each day the company has available 140 man-hours for cutting, 120 man-hours for shaping, and 150 man-hours for finishing. How many pairs of each type of ski should the company produce to maximize their profit if a pair of downhil yields a profit of $10 and a pair of cross country skis yields a profit of $8? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #119834 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=119834\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The Slip and Slide Ski Company manufactures downhill skis and cross country skis.<BR>\n" );
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document.write( " A pair of downhill skis requires 2 man-hours for cutting, 1 man-hour for shaping, and 3 man-hours for finishing;<BR>\n" );
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document.write( "a pair of cross country skis requires 2 man-hours for cutting, 2 man-hours for shaping, and 1 man-hour for finishing.<BR>\n" );
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document.write( " Each day the company has available 140 man-hours for cutting, 120 man-hours for shaping, and 150 man-hours for finishing.<BR>\n" );
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document.write( "Cutting Inequality: 2d + 2c <= 140<BR>\n" );
document.write( "Shaping Inequality: 1d + 2c <= 120<BR>\n" );
document.write( "Finishg Inequality: 3d + 1c <= 150<BR>\n" );
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document.write( "How many pairs of each type of ski should the company produce to maximize their profit if a pair of downhill yields a profit of $10 and a pair of cross country skis yields a profit of $8?<BR>\n" );
document.write( "Total profit = 10d + 8c<BR>\n" );
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document.write( "Let \"c\" be the dependent variable and \"d\" be the independent variable:<BR>\n" );
document.write( "c >= 0<BR>\n" );
document.write( "d >= 0<BR>\n" );
document.write( "c <= -d + 70<BR>\n" );
document.write( "c <= -(1/2)d + 60<BR>\n" );
document.write( "c <= -3d + 150<BR>\n" );
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document.write( "Graph the three inequalities and note the coordinates of the vertices in<BR>\n" );
document.write( "the 1st Quadrant:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C50%2C-10%2C170%2C-x%2B70%2C%28-1%2F2%29x%2B60%2C-3x%2B150%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-10%2C50%2C-10%2C170%2C-x%2B70%2C%28-1%2F2%29x%2B60%2C-3x%2B150%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "I'm going to assume you know you need to find the coordinates of the<BR>\n" );
document.write( "intersection of each pair of equations. You get these coordinate pairs:<BR>\n" );
document.write( "P = 10d + 8c<BR>\n" );
document.write( "(0,60) has a P value of 480 <BR>\n" );
document.write( "(50,0) has a P value of 500<BR>\n" );
document.write( "(20,50) has a P value of 600<BR>\n" );
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document.write( "Ans: Maximum Profit if c=50 and d=20<BR>\n" );
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document.write( "Comment: I recommend you check the arithmetic carefully.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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