document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190768>Question 1190768</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Randy can invest up to $40,000. As his financial advisor, you recommend that he place at least $10,000 in Account A yielding 2% and at most $20,000 in Account B yielding 5%. (i) Using x to denote the amount of money invested in Account A and y to denote the amount of money invested in Account B, write a system of linear inequalities that describes the possible amounts of each investments. Assume x and y are in thousands of dollars.   [4] <BR>\n" );
document.write( "(ii)	Graph the system of inequalities  	 	 	 	 	 	 	[6] <BR>\n" );
document.write( "(iii)	Given that the objective function can be written as I=0.02x + 0.05y (where I represents income), determine how much money should be placed in each investment so that his income is <BR>\n" );
document.write( "maximized. 	 <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #822473 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=822473\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = 2% investment<BR>\n" );
document.write( "y = 5% investment\r<BR>\n" );
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document.write( "constraints are:<BR>\n" );
document.write( "x >= 10<BR>\n" );
document.write( "y <= 20<BR>\n" );
document.write( "x + y <= 40<BR>\n" );
document.write( "x >= 0<BR>\n" );
document.write( "y >= 0<BR>\n" );
document.write( "objective function is:<BR>\n" );
document.write( "profit = .02x + .05y\r<BR>\n" );
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document.write( "using the desmos.com calculator, you would:<BR>\n" );
document.write( "graph the opposite of the inequalities.<BR>\n" );
document.write( "the area of the graph that is not shaded is you region of feasibility.<BR>\n" );
document.write( "the corner points of the region of feasibility are where yoour maximum solution lies.<BR>\n" );
document.write( "evaluate the objective function at each of these corner point.\r<BR>\n" );
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document.write( "this is what the graph looks like:\r<BR>\n" );
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document.write( "your corner points are:<BR>\n" );
document.write( "(10,0)<BR>\n" );
document.write( "(10,20)<BR>\n" );
document.write( "(20,20)<BR>\n" );
document.write( "(40,0)\r<BR>\n" );
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document.write( "at (10,0), the profit is .02 * 10 + .05 * 0 = .2 * 1000 = 200<BR>\n" );
document.write( "at (10,20), the profit is .02 * 10 + .05 * 20 = 1.2 * 1000 = 1200<BR>\n" );
document.write( "at (20,20), the profit is  .02 * 20 + .05 * 20 = 1.4 * 1000 = 1400<BR>\n" );
document.write( "at (40,0), the profit is .02 * 40 + .05 * 0 = .8 * 1000 = 800\r<BR>\n" );
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document.write( "your maximum profit is when x = 20 and y = 20.<BR>\n" );
document.write( "that would be 20,000 invested in account A and 20,000 invested in account B.<BR>\n" );
document.write( ".02 * 20,000 + .05 * 20,000 = 1400.\r<BR>\n" );
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document.write( "all your constraints need to be satisfied at that corner point.\r<BR>\n" );
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document.write( "at (20,20):<BR>\n" );
document.write( "x >= 10 is satisfied.<BR>\n" );
document.write( "y <= 20 is satisfied.<BR>\n" );
document.write( "x + y <= 40 is satisfied.<BR>\n" );
document.write( "x >= 0 is satisfied.<BR>\n" );
document.write( "y >= 0 is satisfied.\r<BR>\n" );
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document.write( "let me know if you have any questions. </SPAN>\n" );
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