document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1092819>Question 1092819</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A city government has approved the construction of an $800 million sports arena. Up to $480 million will be raised by selling bonds that pay simple interest at a rate of 4% annually. The remaining amount (up to $640 million) will be obtained by borrowing money from an insurance company at a simple interest rate of 2%. Determine whether the arena can be financed so that the annual interest is $21 million. (If there is no solution, enter NO SOLUTION.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #707480 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=707480\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> there is a feasible solution.\r<BR>\n" );
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document.write( "that solution is when x = 250 and y = 550\r<BR>\n" );
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document.write( "x represents the number of dollars in bonds that require payment of 4% interest.\r<BR>\n" );
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document.write( "y represents the number of dollars in loans from an insurance company that require payment of 2% interest.\r<BR>\n" );
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document.write( "the total number of dollars raised is x + y = 250 + 550 = 800 million.\r<BR>\n" );
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document.write( "the interest requirement on the number of dollars raised through issuance of bonds is 250 * .04 = 10 million.\r<BR>\n" );
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document.write( "the interest requirement on the number of dollars raised through the insurance company is 550 * .02 =  11 million.\r<BR>\n" );
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document.write( "the total interest requirement is 21 million.\r<BR>\n" );
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document.write( "this was found by finding the intersection of the following equations:\r<BR>\n" );
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document.write( "x + y = 800\r<BR>\n" );
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document.write( ".04x + .02y = 21\r<BR>\n" );
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document.write( "these equations are solved simultaneously.\r<BR>\n" );
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document.write( "we'll solve by substitution.\r<BR>\n" );
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document.write( "in the first equation, solve for y to get y = 800 - x.\r<BR>\n" );
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document.write( "in the second equation, replace y with 800 - x to get .04 * x + .02 * (800 - x) = 21\r<BR>\n" );
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document.write( "simplify this second equaton to get .04 * x + .02 * 800 - .02 * x = 21\r<BR>\n" );
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document.write( "simplify further and combine like terms to get .02 * x + 16 = 21\r<BR>\n" );
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document.write( "subtract 16 from both sides of the equation to get .02 * x = 5\r<BR>\n" );
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document.write( "solve for x to get x = 5 / .02 = 250.\r<BR>\n" );
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document.write( "since x + y = 800 and x = 250, then y has to be equal to 550.\r<BR>\n" );
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document.write( "your intersection is when x = 250 and y = 550\r<BR>\n" );
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document.write( "the next step is to see if this meets the requirements of the problem.\r<BR>\n" );
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document.write( "your constraints are that x <= 480 and y <= 640.\r<BR>\n" );
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document.write( "these constraints are met.\r<BR>\n" );
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document.write( "x + y = 800<BR>\n" );
document.write( ".04x + .02y = 21\r<BR>\n" );
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document.write( "these requirements are met.\r<BR>\n" );
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document.write( "another constraint is that x and y both have be greater than or equal to 0.\r<BR>\n" );
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document.write( "these constraint have also been met.\r<BR>\n" );
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document.write( "graphically, your solution looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/090811.jpg\"alt=\"$$$\" >\r<BR>\n" );
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document.write( "the point (250,550) is at the intersection of the lines of the equations of x + y = 800 and .04x + .02y = 21.\r<BR>\n" );
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document.write( "you can see that x-coordinate of 250 is smaller than x = 480 and you can see that the y-coordinate of 550 is smaller than y = 640.\r<BR>\n" );
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document.write( "you can also see that these values are both greater than 0.\r<BR>\n" );
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document.write( "therefore, the solution is feasible because you have an intersection of the required equations and that solution is in the feasible region.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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