document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205691>Question 1205691</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Egypt Co. offers to the market two types of gadgets. Regarding the nature of the<BR>\n" );
document.write( "production process, and there are not more than 60 hours of the whole operation process. A gadget of the regular type requires 1 hour of completing, while a premium gadget needs 3 hours of finishing. To keep the production alive, Egypt Co. must make at least 10 gadgets a day. The contribution of $3 is realized for each regular gadget and $9 for a premium gadget. The historical record suggests that the demand of premium gadget is increasing and is at least the demand of regular ones. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842664 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=842664\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = the number of regular gadgets.<BR>\n" );
document.write( "y = the number of premium gadgets.\r<BR>\n" );
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document.write( "you get 3 dollars for every regular gadget and 9 dollars for every premium gadgets.\r<BR>\n" );
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document.write( "your constraint inequalities are:<BR>\n" );
document.write( "x + y >= 10 <BR>\n" );
document.write( "x + 3y <= 60<BR>\n" );
document.write( "y >= x<BR>\n" );
document.write( "x >= 0<BR>\n" );
document.write( "y >= 0\r<BR>\n" );
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document.write( "your objective function is:<BR>\n" );
document.write( "3x + 9y which you want to maximize.\r<BR>\n" );
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document.write( "using the desmod.com calculator at <a  rel=nofollow HREF= \"https://www.desmos.com/calculator\" target = \"_blank\">https://www.desmos.com/calculator</a>, you would:\r<BR>\n" );
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document.write( "graph the opposite of the inequalities.<BR>\n" );
document.write( "the area on the graph that is not shaded is your region of feasibility.<BR>\n" );
document.write( "you evaluate the objective function at each corner point of that region to find the corner point with the maximum contribution.\r<BR>\n" );
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document.write( "it appears that the coordinate points of (0,20) and (15,15) both contain the maximum contribution at 180 dollars each.\r<BR>\n" );
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document.write( "you would then decide which one of those you want to do based on other considerations, such as maybe you don't want to just make premium gadgets since there's a market for the regular gadgets as well.\r<BR>\n" );
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document.write( "here's what the graph looks like.\r<BR>\n" );
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document.write( "all the constraint inequalities are asatisfied at each corner point, as they should be.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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