document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1135748>Question 1135748</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 	The following information relate to Kathurima Ltd, a dealer in standard wooden furniture on the outskirts of the city of Nairobi. The company realized profits of Sh. 120,000 from 7 tables, Sh. 124,000 from 9 tables and Sh. 113,000 from 4 tables made and sold. Kathurima has now approached you for assistance in forecasting future profits. The profit function is believed to be quadratic in nature. What will be Kathurima Ltd’s profit function to be used in forecasting? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #753442 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=753442\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The ordered pairs (using thousands of Sh.) are (4, 113) (7, 120) and (9, 124) <BR>\n" );
document.write( "put these into ax^2+bx+c=y<BR>\n" );
document.write( "so 16a+4b+c=113<BR>\n" );
document.write( "49a+7b+c=120 and<BR>\n" );
document.write( "81a+9b+c=124\r<BR>\n" );
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document.write( "The first and second give <BR>\n" );
document.write( "-112a-28b-7c=-791<BR>\n" );
document.write( "196a+28b+4c=480<BR>\n" );
document.write( "84a-3c=-311\r<BR>\n" );
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document.write( "first and third give<BR>\n" );
document.write( "-144a-36b-9c=-1017<BR>\n" );
document.write( "324a+36b+4c=496<BR>\n" );
document.write( "180a-5c=-521<BR>\n" );
document.write( "those two become<BR>\n" );
document.write( "420a-15c=-1555<BR>\n" );
document.write( "-540a+15c=1563<BR>\n" );
document.write( "-120a=8<BR>\n" );
document.write( "a=-(1/15) or -0.0667<BR>\n" );
document.write( "therefore 4b+c=113+16/15=114.0667 (114.1)<BR>\n" );
document.write( "and (third) 9b+c=131.4<BR>\n" );
document.write( "-5b=-17.3<BR>\n" );
document.write( "b=3.46\r<BR>\n" );
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document.write( "c=100.26<BR>\n" );
document.write( "the equation is -0.0667x^2+3.46x+100.26=f(x)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-5%2C25%2C-10%2C150%2C+-0.0667x%5E2%2B3.46x%2B100.26%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-5%2C25%2C-10%2C150%2C+-0.0667x%5E2%2B3.46x%2B100.26%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > in THOUSANDS of Sh. </SPAN>\n" );
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