document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1173374>Question 1173374</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A small manufacturing makes and sells x machines each month. The monthly cost, C ,in dollars, of making x dollars is given by<BR>\n" );
document.write( "C(x)= 0.35x^2 + 3200<BR>\n" );
document.write( "The monthly revenue, R, in dollars, obtained by selling x machines is given by<BR>\n" );
document.write( "R(x)= 180x - 0.55x^2\r<BR>\n" );
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document.write( "Find the smallest number of machines the company must make and sell each month in order to make a positive profit. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #798823 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=798823\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A small manufacturing makes and sells x machines each month.<BR>\n" );
document.write( " The monthly cost, C ,in dollars, of making x dollars is given by<BR>\n" );
document.write( "C(x)= 0.35x^2 + 3200<BR>\n" );
document.write( "The monthly revenue, R, in dollars, obtained by selling x machines is given by<BR>\n" );
document.write( "R(x)= 180x - 0.55x^2<BR>\n" );
document.write( "Find the smallest number of machines the company must make and sell each month in order to make a positive profit.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Revenue > cost<BR>\n" );
document.write( "180x - .55x^2 > .35x^2 + 3200<BR>\n" );
document.write( "-.55x^2 - .35x^2 + 180x - 3200 > 0<BR>\n" );
document.write( "-.90x^2 + 180x - 3200 > 0<BR>\n" );
document.write( "the quadratic formula gives us two solutions<BR>\n" );
document.write( "x > 180.3<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x > 19.7<BR>\n" );
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document.write( "For least number of machines lets use x = 20 units<BR>\n" );
document.write( "Revenue: 180(20) - .55*(20^2) = 3380<BR>\n" );
document.write( "Cost: .35(20^2) + 3200 = 3060<BR>\n" );
document.write( "a profit of  $320<BR>\n" );
document.write( "however is you use x=19 machines<BR>\n" );
document.write( "Rev: 180(19) - .55(19^2) = 3221.45<BR>\n" );
document.write( "Cost: .35(19^2) + 3200 = 3326.35<BR>\n" );
document.write( "a loss of about $105<BR>\n" );
document.write( ":<BR>\n" );
document.write( "20 units the least to make a profit\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );