document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1125335>Question 1125335</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find two positive numbers satisfying the given requirements.<BR>\n" );
document.write( "The sum of the first and twice the second is 120 and the product is a maximum. </SPAN>\n" );
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document.write( "Let the numbers be x and y.  Then we know<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2y=120 ALIGN=MIDDLE  ALT=\"x%2B2y=120\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y+=+120-x ALIGN=MIDDLE  ALT=\"2y+=+120-x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+60-x%2F2 ALIGN=MIDDLE  ALT=\"y+=+60-x%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So the second number is 60-x/2.<br><BR>\n" );
document.write( "We want the product of the two numbers to be a maximum.  The product is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2860-x%2F2%29+=+-%281%2F2%29x%5E2%2B60x ALIGN=MIDDLE  ALT=\"x%2860-x%2F2%29+=+-%281%2F2%29x%5E2%2B60x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The maximum/minimum value of the quadratic expression ax^2+bx+c is when x = -b/2a.  In this problem, that is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-60%2F-1+=+60 ALIGN=MIDDLE  ALT=\"-60%2F-1+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So the first number is 60 and the second is 60-30 = 30.  The product is 1800. </SPAN>\n" );
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