document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=5766>Question 5766</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The vending machine on the fourth floor of your building sells bottles of soft drink at a price of $1 per bottle. Let X denote the number of bottles of soft drink sold each week.<BR>\n" );
document.write( "A) What is the revenue function: R(x) = ?<BR>\n" );
document.write( "B) If the fixed cost for the owner of this vending machine is $125 per week, and the wholesale cost of each bottle is 50 cents, what is the total cost function: C(x) = ?<BR>\n" );
document.write( "C) What is the profit function: P(x) = ?<BR>\n" );
document.write( "D) What is the Break- Even Point: BEP = ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #2966 by </B><A HREF=/tutors/aboutme.mpl?userid=Abbey><B>Abbey(339)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Abbey><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=2966\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = the number of bottles sold<BR>\n" );
document.write( "Revenue will equal $1 multiplied by the number of bottles sold,<BR>\n" );
document.write( "R(x)=$1(x)<BR>\n" );
document.write( "The fixed cost for the owner is $125 and the wholesale cost is 50 cents.<BR>\n" );
document.write( "To create the cost function C(x), multiply the number of bottles sold by 50 cents and add $125 to the total:<BR>\n" );
document.write( "C(x) = $.50(x) + $125<BR>\n" );
document.write( "The profit function is the revenue function - the cost function:<BR>\n" );
document.write( "P(x)=$1(x)-($.50(x)+$125)<BR>\n" );
document.write( "Finally, the break even point will be when the revenue is equal to the cost:<BR>\n" );
document.write( "$1x=$.50(x)+$125<BR>\n" );
document.write( "convert the dollars and cents into fractions and integers:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28x%2F2%29%2B125 ALIGN=MIDDLE  ALT=\"x=%28x%2F2%29%2B125\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F2 ALIGN=MIDDLE  ALT=\"x%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides of the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-%28x%2F2%29=125 ALIGN=MIDDLE  ALT=\"x-%28x%2F2%29=125\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2F2%29+=+125 ALIGN=MIDDLE  ALT=\"%28x%2F2%29+=+125\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply both sides by 2:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=250 ALIGN=MIDDLE  ALT=\"x=250\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so the break even point occurs when 250 cans of soft drinks have been sold.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This makes sense because if the machine sells 250 cans of soda, it has earned $250.  the cost of 250 cans is $125 + the fixed cost of $125 = $250.<BR>\n" );
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