document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1107689>Question 1107689</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A machine comes in 2 sections. The weights of the section are x kg and b kg. The cost, c, of the machine (in dollars) is given by c=2x+b. The earning capacity, y, of the machine is given by y=x(x+b). If c has the fixed value 10, express y as a function of x and hence find the value of x for which y is a maximum. Find the maximum value of y. [Please do not use differentiation]. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #722747 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=722747\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you have 2 equations.\r<BR>\n" );
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document.write( "c = 2x + b is the first equation.\r<BR>\n" );
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document.write( "y = x * (x + b) is the second equation.\r<BR>\n" );
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document.write( "you are given that c = 10 which makes the first equation 10 = 2x + b.\r<BR>\n" );
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document.write( "if you solve this first equation for b, you get b = 10 - 2x.\r<BR>\n" );
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document.write( "replace b in the second equation with this to get y = x * (x + 10 - 2x).\r<BR>\n" );
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document.write( "simplify that to get y = x * (10 - x).\r<BR>\n" );
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document.write( "simplify further to get y = 10x - x^2.\r<BR>\n" );
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document.write( "reorder the terms in descending order of degree to get y = -x^2 + 10x.\r<BR>\n" );
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document.write( "that's a quadratic equation in the form of y = ax^2 + bx + c.\r<BR>\n" );
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document.write( "in that equation, a = -1 and b= 10.\r<BR>\n" );
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document.write( "the maximum value of y in that equation is when x = -b/2a.\r<BR>\n" );
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document.write( "this results in x = -10/-2 which results in x = 5.\r<BR>\n" );
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document.write( "when x = 5, the value of y is equal to -5^2 + 10*5= -25 + 50 = 25.\r<BR>\n" );
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document.write( "your maximum value of y should be 25.\r<BR>\n" );
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document.write( "if you graph the equation of y = -x^2 + 10x, it will look like this.\r<BR>\n" );
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document.write( "you can see that the maximum value of the equation is y = 25 when x = 5.\r<BR>\n" );
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