document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=390216>Question 390216</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A factory finds that it's daily profit, y dollars, is related to x, the number of items it produces daily where y = -x^2 + 90x.<BR>\n" );
document.write( "a) Draw the graph of y = -x^2 + 90x.<BR>\n" );
document.write( "b) Use this graph to find<BR>\n" );
document.write( "i) the number of items the factory must produce daily in order to maximize profit,<BR>\n" );
document.write( "ii) the maximum profit. \r<BR>\n" );
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document.write( "=) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #276636 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=276636\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A factory finds that it's daily profit, y dollars, is related to x, the number of items it produces daily where y = -x^2 + 90x.<BR>\n" );
document.write( "a) Draw the graph of y = -x^2 + 90x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28300%2C300%2C-20%2C100%2C-2500%2C2500%2C%28-x%5E2%2B90x%29%29 ALIGN=MIDDLE  ALT=\"+graph%28300%2C300%2C-20%2C100%2C-2500%2C2500%2C%28-x%5E2%2B90x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b) Use this graph to find\r<BR>\n" );
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document.write( "i) the number of items the factory must produce daily in order to maximize profit,<BR>\n" );
document.write( "At x = 45 it peaks and then drops.The maximum it should produce is 45 items.\r<BR>\n" );
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document.write( "From: mananth@hotmail.com<BR>\n" );
document.write( "To: ahmad.tehseen@hotmail.com<BR>\n" );
document.write( "Subject: RE: Thank you note (algebra.com problem 390216)<BR>\n" );
document.write( "Date: Mon, 3 Jan 2011 21:29:58 +0530\r<BR>\n" );
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document.write( "Firstly you know that it is a parabola.<BR>\n" );
document.write( "the co-efficient of x^2=- so the parabola opens downwards.<BR>\n" );
document.write( "for y = 0 you have 2 values of x.<BR>\n" );
document.write( "y =-x^2 +90x<BR>\n" );
document.write( "y=-x(x-90)<BR>\n" );
document.write( " <BR>\n" );
document.write( "x= 0 & x=90<BR>\n" );
document.write( "you have two points (0,0) & (0,90)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "find the vertex<BR>\n" );
document.write( "x co-ordinate = -b/2a in the equation ax^2+bx +c<BR>\n" );
document.write( "x co-ordinate= -90/-2<BR>\n" );
document.write( "x co-ordinate = 45<BR>\n" );
document.write( "..<BR>\n" );
document.write( "when you put the equation in (x-h)^2 +k <BR>\n" );
document.write( "you get the value of k which is the y co-ordinate of the vertex.<BR>\n" );
document.write( "y= (-x^2+90x) -45^2 +45^2<BR>\n" );
document.write( "y=-1(x^2-90x+45^2) +45^2<BR>\n" );
document.write( "y=-1(x-45)^2+2025<BR>\n" );
document.write( "vertex = (45,2025)<BR>\n" );
document.write( "The y value when production = 45 units is 2025 . The maximum profit.<BR>\n" );
document.write( "You have three values including vertex.<BR>\n" );
document.write( "plot a few points with x <45 & > 45 . Find y co-ordinates . draw the curve.<BR>\n" );
document.write( "Generally students use a graphic calculator to get the points.<BR>\n" );
document.write( "(0,0) & (0,90) (45,2025)<BR>\n" );
document.write( " <BR>\n" );
document.write( "ur mails are bouncing so I can't clarify your doubts<BR>\n" );
document.write( "Happy new year<BR>\n" );
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