document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199213>Question 1199213</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A candy manufacturer makes two types of special candy, say A and B. Candy A consists of equal<BR>\n" );
document.write( "part of dark chocolate and caramel and Candy B consists of two parts of dark chocolate and one\r<BR>\n" );
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document.write( "part of walnut. The company has in stock 430 kilograms of caramel, 360 kilograms of dark\r<BR>\n" );
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document.write( "chocolate, and 210 kilograms of walnuts. The company sells Candy A for P285 and Candy B for\r<BR>\n" );
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document.write( "P260 per kilograms. How much of each candy should the manufacturer produce to maximize profit?​ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832994 by </B><A HREF=/tutors/aboutme.mpl?userid=Shin123><B>Shin123(626)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Shin123><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=Shin123><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=832994\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > be the amount (in kilograms) of Candy A that is produced, and let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > be the amount of Candy B that is produced. The profit that the manufacturer makes is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=285x%2B260y ALIGN=MIDDLE  ALT=\"285x%2B260y\"   DISABLED_style= \"max-width:90%; height:auto;\" >. However, the constraints are that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=430 ALIGN=MIDDLE  ALT=\"x%3C=430\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2y%3C=360 ALIGN=MIDDLE  ALT=\"x%2B2y%3C=360\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C=210 ALIGN=MIDDLE  ALT=\"y%3C=210\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "We can see that it is optimal to have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2y=360 ALIGN=MIDDLE  ALT=\"x%2B2y=360\"   DISABLED_style= \"max-width:90%; height:auto;\" >, since moving it off of that line would only decrease the profit. Multiplying both sides of that by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=130 ALIGN=MIDDLE  ALT=\"130\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=130x%2B260y=46800 ALIGN=MIDDLE  ALT=\"130x%2B260y=46800\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Adding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=155x ALIGN=MIDDLE  ALT=\"155x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides, we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=285x%2B260y=155x%2B46800 ALIGN=MIDDLE  ALT=\"285x%2B260y=155x%2B46800\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We can see that we got out profit into a form that doesn't involve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > at all, so we should just maximize <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The highest value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > that satisfies all of the constriants is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=360 ALIGN=MIDDLE  ALT=\"x=360\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Therefore, the candy manufacturer should produce <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360 ALIGN=MIDDLE  ALT=\"360\"   DISABLED_style= \"max-width:90%; height:auto;\" > kilograms of Candy A, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > kilograms of Candy B. </SPAN>\n" );
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