document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1174707>Question 1174707</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An investor has up to $250,000 to invest in three types of investments. Type A pays 8% annually and has a risk factor of<BR>\n" );
document.write( "0. Type B pays 10% annually and has a risk factor of 0.06.<BR>\n" );
document.write( "Type C pays 14% annually and has a risk factor of 0.10. To<BR>\n" );
document.write( "have a well-balanced portfolio, the investor imposes the following conditions. The average risk factor should be no<BR>\n" );
document.write( "greater than 0.05. Moreover, at least one-fourth of the total<BR>\n" );
document.write( "portfolio is to be allocated to Type A investments and at least<BR>\n" );
document.write( "one-fourth of the portfolio is to be allocated to Type B investments. How much should be allocated to each type of investment to obtain a maximum return? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #800745 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=800745\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i'm not totally sure, but i think the problem needs to be stated as:\r<BR>\n" );
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document.write( "let a = the amount of money invested in the type A investment.<BR>\n" );
document.write( "let b = the amount of money invested in the type B investment.<BR>\n" );
document.write( "let c = the amount of money invested in the type C investment.\r<BR>\n" );
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document.write( "you want to maximize the return, so your objective function is:\r<BR>\n" );
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document.write( "return = .08a + .10b + .14c.<BR>\n" );
document.write( "this is what you want to maximize.\r<BR>\n" );
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document.write( "your constraints are:\r<BR>\n" );
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document.write( "a + b + c <= 250000<BR>\n" );
document.write( "total investment must be less than or equal to 250,000.\r<BR>\n" );
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document.write( "a >= .25 * 250000 <BR>\n" );
document.write( "at least one quarter of the total investment must be in type A.\r<BR>\n" );
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document.write( "b >= .25 * 250000<BR>\n" );
document.write( "at least one quarter of the total investment must be in type B.\r<BR>\n" );
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document.write( "0a + .06b + .10c <= .05 * 250000<BR>\n" );
document.write( "the average risk factor must be smaller than or equal to .05 * the investment.\r<BR>\n" );
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document.write( "it's that last constraint i'm not very sure about, but i couldn't think of any other way to apply it.\r<BR>\n" );
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document.write( "i used a simplex method tool to find the optimum solution.\r<BR>\n" );
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document.write( "that tool can be found at <a  rel=nofollow HREF= \"https://www.zweigmedia.com/RealWorld/simplex.html\" target = \"_blank\">https://www.zweigmedia.com/RealWorld/simplex.html</a>\r<BR>\n" );
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document.write( "the results of using that tool are shown below.\r<BR>\n" );
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document.write( "the results show that your maximum return on the invewtment will be 26,500.<BR>\n" );
document.write( "that's the value for the variable p.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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