document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=127434>Question 127434</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Outdoor Furniture Corporation manufactures two products, benches and picnic tables, for use in yards and parks. The firm has two main resources: its carpenters (labor force) and a supply of redwood for use in the furniture. During the next production cycle, 1,200 hours of labor are available under a union agreement. The firm also has a stock of 3,500 feet of good quality redwood. Each bench that Outdoor Furniture produces requires 4 labor hours and 10 feet of redwood: each picnic table takes 6 labor hours and 35 feet of redwood. Completed benches will yield a profit of $9 each, and tables will result in a profit of $20 each. How many benches and tables should Outdoors Furniture produce to obtain the largest possible profit? Use graphical Linear programming approach. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #93449 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=93449\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> During the next production cycle, 1,200 hours of labor are available under a union agreement. <BR>\n" );
document.write( "The firm also has a stock of 3,500 feet of good quality redwood.<BR>\n" );
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document.write( "Let # of benches produced be \"b\"; Let # of picnic tables produced be \"P\". <BR>\n" );
document.write( "Each bench that Outdoor Furniture produces requires 4 labor hours and 10 feet of redwood: <BR>\n" );
document.write( "each picnic table takes 6 labor hours and 35 feet of redwood. <BR>\n" );
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document.write( "Labor Inequality: 4b+6p <= 1200<BR>\n" );
document.write( "Redwood Inequality: 10b+35p <= 3500\r<BR>\n" );
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document.write( "Completed benches will yield a profit of $9 each, and tables will result in a profit of $20 each.<BR>\n" );
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document.write( "Objective Function: Profit = 9b+20p<BR>\n" );
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document.write( "How many benches and tables should Outdoors Furniture produce to obtain the largest possible profit? Use graphical Linear programming approach.<BR>\n" );
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document.write( "INEQUALITIES:<BR>\n" );
document.write( "Labor: p <= (-2/3)b + 200<BR>\n" );
document.write( "Redwood: p <= (-2/7)b + 100<BR>\n" );
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document.write( "Graph the solution sets of both inequalities:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C320%2C-10%2C220%2C%28-2%2F3%29x%2B200%2C%28-2%2F7%29x%2B100%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-10%2C320%2C-10%2C220%2C%28-2%2F3%29x%2B200%2C%28-2%2F7%29x%2B100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Determine the vertices of the solution set:<BR>\n" );
document.write( "(0,100), (262.5,25) (300,0)<BR>\n" );
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document.write( "Check each vertex pair in the objective function to see which pair<BR>\n" );
document.write( "yields the maximum profit.<BR>\n" );
document.write( "Profit = 9b+20p<BR>\n" );
document.write( "(0,100) yields: 2000<BR>\n" );
document.write( "(262.5,25) yields: 9*262.5+20*25=2862.50<BR>\n" );
document.write( "(300,0) yields 9*300 = 2700<BR>\n" );
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document.write( "Conclusion: maximum comes with 263 benches and 25 picnic tables.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
document.write( " </SPAN>\n" );
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