document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=289772>Question 289772</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello can anyone help solve this problem with work shown and answers it will help me learn how to do these problems for my upcoming test.\r<BR>\n" );
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document.write( "Sean's Widget Company has revenue that is modeled by the function R(x) = -4x2 + 35x and costs modeled by the function C(x) = 12x +30. The input variable x is in hundreds of widgets, and the outputs of the functions are in units of thousands of dollars.  Construct a profit function P(x) and find the value of x that maximizes the profit. \r<BR>\n" );
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document.write( "Thank you John </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #209815 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=209815\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Sean's Widget Company has revenue that is modeled by the <BR>\n" );
document.write( "function R(x) = -4x2 + 35x and costs modeled by the function C(x) = 12x +30. <BR>\n" );
document.write( "The input variable x is in hundreds of widgets, and the outputs of the <BR>\n" );
document.write( "functions are in units of thousands of dollars.<BR>\n" );
document.write( " Construct a profit function P(x) and find the value of x that maximizes the profit. <BR>\n" );
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document.write( "Profit = Revenue - Cost<BR>\n" );
document.write( "P(x) = R(x) - C(x)<BR>\n" );
document.write( "Which is<BR>\n" );
document.write( "P(x) = -4x^2 + 35x - (12x + 30)<BR>\n" );
document.write( "Removing the bracket changes the signs<BR>\n" );
document.write( "P(x) = -4x^2 + 35x - 12x - 30<BR>\n" );
document.write( "Combine like terms<BR>\n" );
document.write( "P(x) = -4x^2 + 23x - 30<BR>\n" );
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document.write( "A quadratic equation, we can find the axis of symmetry: x = -b/(2a)<BR>\n" );
document.write( "That value of x will give us max profit<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-23%29%2F%282%2A-4%29 ALIGN=MIDDLE  ALT=\"%28-23%29%2F%282%2A-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-23%29%2F%28-8%29 ALIGN=MIDDLE  ALT=\"%28-23%29%2F%28-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = +2.875 hundreds of widgets<BR>\n" );
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document.write( " 287.5 ~ 288 widgets for max profit (has to be an integer)<BR>\n" );
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document.write( "To find the actual profit value (in thousands), substitute 2.88 for x in the<BR>\n" );
document.write( "equation P(x) = -4(2.88^2) + 23(2.88) - 30 </SPAN>\n" );
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