document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=110305>Question 110305</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many packs of each hot dogs should be made to maximize profits and what is the profits?\r<BR>\n" );
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document.write( "all-beef hot dogs - 1 package requires 1 lb of beef<BR>\n" );
document.write( "regular hot dogs - 1 package requires 1/2 lb of beef and 1/2 lb of pork\r<BR>\n" );
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document.write( "40 cent profit on each package of all-beef hot dogs<BR>\n" );
document.write( "30 cent profit on each package of regular hot dogs\r<BR>\n" );
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document.write( "200 lbs of beef and 150 lbs of pork are available  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #80394 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=80394\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = packages of reg hotdogs produced<BR>\n" );
document.write( "y = packages of beef hotdogs produced<BR>\n" );
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document.write( "all-beef hot dogs - 1 package requires 1 lb of beef<BR>\n" );
document.write( "regular hot dogs - 1 package requires 1/2 lb of beef and 1/2 lb of pork<BR>\n" );
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document.write( "200 lbs of beef and 150 lbs of pork are available<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5Bmax%5D ALIGN=MIDDLE  ALT=\"y%5Bmax%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 200 lbs / 1 lb<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5Bmax%5D+=+200 ALIGN=MIDDLE  ALT=\"y%5Bmax%5D+=+200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Bmax%5D ALIGN=MIDDLE  ALT=\"x%5Bmax%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 150 lbs / .5 lbs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Bmax%5D+=+300 ALIGN=MIDDLE  ALT=\"x%5Bmax%5D+=+300\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is because once you run out of pork, the leftover<BR>\n" );
document.write( "beef does you no good<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+0 ALIGN=MIDDLE  ALT=\"x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5Bmax%5D+=+200 ALIGN=MIDDLE  ALT=\"y%5Bmax%5D+=+200\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is the most y can be<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+50 ALIGN=MIDDLE  ALT=\"x+=+50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5Bmax%5D+=+175 ALIGN=MIDDLE  ALT=\"y%5Bmax%5D+=+175\"   DISABLED_style= \"max-width:90%; height:auto;\" > this is 200 - 25<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+100 ALIGN=MIDDLE  ALT=\"x+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5Bmax%5D+=+150 ALIGN=MIDDLE  ALT=\"y%5Bmax%5D+=+150\"   DISABLED_style= \"max-width:90%; height:auto;\" > this is 200 - 50<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+150 ALIGN=MIDDLE  ALT=\"x+=+150\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5Bmax%5D+=+125 ALIGN=MIDDLE  ALT=\"y%5Bmax%5D+=+125\"   DISABLED_style= \"max-width:90%; height:auto;\" > this is 200 - 75<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+200 ALIGN=MIDDLE  ALT=\"x+=+200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5Bmax%5D+=+100 ALIGN=MIDDLE  ALT=\"y%5Bmax%5D+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" > this is 200 - 100<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+250 ALIGN=MIDDLE  ALT=\"x+=+250\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5Bmax%5D+=+75 ALIGN=MIDDLE  ALT=\"y%5Bmax%5D+=+75\"   DISABLED_style= \"max-width:90%; height:auto;\" > this is 200 - 125<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+300 ALIGN=MIDDLE  ALT=\"x+=+300\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5Bmax%5D+=+50 ALIGN=MIDDLE  ALT=\"y%5Bmax%5D+=+50\"   DISABLED_style= \"max-width:90%; height:auto;\" > this is 200 - 150<BR>\n" );
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document.write( "Now list the profit in each case<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.3%2A0+%2B+.4%2A200+=+80 ALIGN=MIDDLE  ALT=\".3%2A0+%2B+.4%2A200+=+80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.3%2A50+%2B+.4%2A175+=+85 ALIGN=MIDDLE  ALT=\".3%2A50+%2B+.4%2A175+=+85\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.3%2A100+%2B+.4%2A150+=+90 ALIGN=MIDDLE  ALT=\".3%2A100+%2B+.4%2A150+=+90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.3%2A150+%2B+.4%2A125+=+95 ALIGN=MIDDLE  ALT=\".3%2A150+%2B+.4%2A125+=+95\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.3%2A200+%2B+.4%2A100+=+100 ALIGN=MIDDLE  ALT=\".3%2A200+%2B+.4%2A100+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.3%2A250+%2B+.4%2A75+=+105 ALIGN=MIDDLE  ALT=\".3%2A250+%2B+.4%2A75+=+105\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.3%2A300+%2B+.4%2A50+=+110 ALIGN=MIDDLE  ALT=\".3%2A300+%2B+.4%2A50+=+110\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "It looks like 300 packages of regular and 50 packages of beef<BR>\n" );
document.write( "hotdogs will maximize profit at $110<BR>\n" );
document.write( "To verify, I'll look at profits with a change of 2 packages for x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.3%2A298+%2B+.4%2A51+=+109.8 ALIGN=MIDDLE  ALT=\".3%2A298+%2B+.4%2A51+=+109.8\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "So it looks like $110 is the maxprofit <BR>\n" );
document.write( "  <BR>\n" );
document.write( " <BR>\n" );
document.write( "     </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );