document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=318406>Question 318406</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A backpack manufacturer produces an internal frame pack and an external frame pack. Let X represent the number of internal frame packs produced in one hour and let Y represent the number of external frame packs produced in one hour. Then the inequalities X+3<18, 2x+y<16 , x>0 , and y>0 describe the constraints for manufacturing both packs. Use the profit function f(X)=50x+80y and the constraints given to determine the maximum profit for manufacturing both backpacks for the given constraints. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #227951 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=227951\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3%3C18 ALIGN=MIDDLE  ALT=\"x%2B3%3C18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C15 ALIGN=MIDDLE  ALT=\"x%3C15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C-2x%2B16 ALIGN=MIDDLE  ALT=\"y%3C-2x%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-2%2C18%2C-2%2C18%2Cgrid%281%29%2Ccircle%288%2C0%2C.4%29%2Ccircle%280%2C16%2C0.4%29%2Ccircle%280%2C0%2C0.4%29%2Cgraph%28300%2C300%2C-2%2C18%2C-2%2C18%2C+-2x%2B16%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "As you can see the constraint, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3%3C18 ALIGN=MIDDLE  ALT=\"x%2B3%3C18\"   DISABLED_style= \"max-width:90%; height:auto;\" > doesn't even enter into calculating the feasible region because the constraint, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2By%3C16 ALIGN=MIDDLE  ALT=\"2x%2By%3C16\"   DISABLED_style= \"max-width:90%; height:auto;\" > really identifies the region. <BR>\n" );
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document.write( "Check the value of the function at the three vertices:<BR>\n" );
document.write( "(0,0):<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f=50x%2B80y=50%280%29%2B80%280%29=0 ALIGN=MIDDLE  ALT=\"f=50x%2B80y=50%280%29%2B80%280%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "(8,0):<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f=50x%2B80y=50%288%29%2B80%280%29=400 ALIGN=MIDDLE  ALT=\"f=50x%2B80y=50%288%29%2B80%280%29=400\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "(0,16):<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f=50x%2B80y=50%280%29%2B80%2816%29=1280 ALIGN=MIDDLE  ALT=\"f=50x%2B80y=50%280%29%2B80%2816%29=1280\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The maximum, 1280, occurs at (0,16). </SPAN>\n" );
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