document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204313>Question 1204313</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose a ceiling fan manufacturer has the total cost function <BR>\n" );
document.write( "C(x) = 37x + 2280<BR>\n" );
document.write( " and the total revenue function <BR>\n" );
document.write( "R(x) = 75x.<BR>\n" );
document.write( "(a) What is the equation of the profit function P(x) for this commodity? <BR>\n" );
document.write( "P(x) =    <BR>\n" );
document.write( " \r<BR>\n" );
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document.write( "(b) What is the profit on 40 units? <BR>\n" );
document.write( "P(40) =  <BR>\n" );
document.write( " \r<BR>\n" );
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document.write( "Interpret your result. <BR>\n" );
document.write( "The total costs are less than the revenue.<BR>\n" );
document.write( "The total costs are more than the revenue.    <BR>\n" );
document.write( "The total costs are exactly the same as the revenue.\r<BR>\n" );
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document.write( "(c) How many fans must be sold to avoid losing money? <BR>\n" );
document.write( "  fans </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840482 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=840482\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose a ceiling fan manufacturer has the total cost function<BR>\n" );
document.write( "C(x) = 37x + 2280<BR>\n" );
document.write( "and the total revenue function<BR>\n" );
document.write( "R(x) = 75x.<BR>\n" );
document.write( "(a) What is the equation of the profit function P(x) for this commodity?<BR>\n" );
document.write( "P(x) =\r<BR>\n" );
document.write( "\n" );
document.write( "(b) What is the profit on 40 units?<BR>\n" );
document.write( "P(40) =\r<BR>\n" );
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document.write( "Interpret your result.<BR>\n" );
document.write( "The total costs are less than the revenue.<BR>\n" );
document.write( "The total costs are more than the revenue.<BR>\n" );
document.write( "The total costs are exactly the same as the revenue.<BR>\n" );
document.write( "(c) How many fans must be sold to avoid losing money?\r<BR>\n" );
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document.write( "Profit function P(x):<BR>\n" );
document.write( "P(x) = R(x) - C(x)<BR>\n" );
document.write( "P(x) = 75x - (37x + 2280)<BR>\n" );
document.write( "P(x) = 75x - 37x - 2280<BR>\n" );
document.write( "P(x) = 38x - 2280\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( " profit on 40 units<BR>\n" );
document.write( "plug x =40<BR>\n" );
document.write( "P(x) = 38x - 2280<BR>\n" );
document.write( "=40*(38)-2280<BR>\n" );
document.write( "= 1520-2280<BR>\n" );
document.write( "=-760<BR>\n" );
document.write( "P(x)=-760<BR>\n" );
document.write( " The company is incurring a loss of $760 when they produce and sell 40 fans. The total costs are greater than the total revenue.\r<BR>\n" );
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document.write( "How many fans must be sold to avoid losing money?\r<BR>\n" );
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document.write( "C(x)=R(x)\r<BR>\n" );
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document.write( "37x + 2280= 75x.<BR>\n" );
document.write( "75x-37x =2280<BR>\n" );
document.write( "38x =2280<BR>\n" );
document.write( "x=60\r<BR>\n" );
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document.write( " The company must sell 60 or more than 60 fans to avoid losing money\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );