document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=623556>Question 623556</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A manufacturer produces a product at a cost of $29.80 per unit. The manufacturer has a fixed cost of $200.00 per day. Each unit retails for $34.00. Let x represent the number of units produced in a 5-day period.\r<BR>\n" );
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document.write( " (a) Write the total cost C as a function of x<BR>\n" );
document.write( "C(x) = ?\r<BR>\n" );
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document.write( "(b) Write the revenue R as a function of x<BR>\n" );
document.write( "R(x) = ?\r<BR>\n" );
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document.write( "(c) Write the profit P as a function of x. (Hint: The profit function is given by by P(x) = R(x) &#8722; C(x).)<BR>\n" );
document.write( "P(x) = ?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #392157 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=392157\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = number of units produced.<BR>\n" );
document.write( "cost per unit = 29.8<BR>\n" );
document.write( "revenue per unit = 34<BR>\n" );
document.write( "fixed cost = 200<BR>\n" );
document.write( "C = Total Cost<BR>\n" );
document.write( "R = Total Revenue<BR>\n" );
document.write( "C = 200 + 29.8*x<BR>\n" );
document.write( "R = 34*x<BR>\n" );
document.write( "P = R - C<BR>\n" );
document.write( "P = 34*x - 29.8*x - 200<BR>\n" );
document.write( "P = 4.2*x - 200<BR>\n" );
document.write( "You don't get a profit until P is greater than or equal to 0.<BR>\n" );
document.write( "You can graph these equations.<BR>\n" );
document.write( "Revenue equation would be y = 34*x<BR>\n" );
document.write( "Cost equation would be y = 29.8*x + 200<BR>\n" );
document.write( "Profit equation would be y = 4.2*x - 200<BR>\n" );
document.write( "Each will be graphed separately below:<BR>\n" );
document.write( "cost equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C100%2C-5%2C3500%2C200%2B29.8%2Ax%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-10%2C100%2C-5%2C3500%2C200%2B29.8%2Ax%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "revenue equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C100%2C-5%2C3500%2C34%2Ax%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-10%2C100%2C-5%2C3500%2C34%2Ax%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "profit equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C100%2C-205%2C350%2C4.2%2Ax-200%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-10%2C100%2C-205%2C350%2C4.2%2Ax-200%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the graphs suggest a break even point at somewhere betweeen 45 and 50.<BR>\n" );
document.write( "calculation of the break even point is shown below:<BR>\n" );
document.write( "this is the point where the revenue equals the cost.<BR>\n" );
document.write( "you get R = C which becomes:<BR>\n" );
document.write( "34*x =  29.8*x + 200<BR>\n" );
document.write( "subtract 29.8*x from both sides of this equation to get:<BR>\n" );
document.write( "34*x - 29.8*x = 200<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "4.20 * x  = 200<BR>\n" );
document.write( "divide both sides by 4.20 to get:<BR>\n" );
document.write( "x =  200 / 4.2 = 47.61904762<BR>\n" );
document.write( "that's your break even point.<BR>\n" );
document.write( "this happens when revenue is equal to 34 * 47.61904762 = 1619.047619.<BR>\n" );
document.write( "this happens when cost is equal to 29.8 * 47.61904762 + 200 = 1619.047619.<BR>\n" );
document.write( "that actual break even point is easier to see if you graph the revenue and cost equations together as shown below:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C100%2C-5%2C3500%2C200%2B29.8%2Ax%2C34%2Ax%2C1619.04%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-10%2C100%2C-5%2C3500%2C200%2B29.8%2Ax%2C34%2Ax%2C1619.04%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a horizontal line at 1619.04 assists you.<BR>\n" );
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