document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=60915>Question 60915</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0072549017/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The cost of producing a number of items x is given by C = mx + b, in which b is the fixed cost and m is the variable cost (the cost of producing one more item).<BR>\n" );
document.write( "(a) If the fixed cost is $40 and the variable cost is $10, write the cost equation.<BR>\n" );
document.write( "(b) Graph the cost equation.<BR>\n" );
document.write( "(c) The revenue generated from the sale of x items is given by R = 50x. Graph the revenue equation on the same set of axes as the cost equation.<BR>\n" );
document.write( "(d) How many items must be produced for the revenue to equal the cost (the break-even point)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #41866 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=41866\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The cost of producing a number of items x is given by C = mx + b, in which b is the fixed cost and m is the variable cost (the cost of producing one more item).<BR>\n" );
document.write( "(a) If the fixed cost is $40 and the variable cost is $10, write the cost equation.<BR>\n" );
document.write( "b=40, m=10<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28C=10x%2B40%29 ALIGN=MIDDLE  ALT=\"highlight%28C=10x%2B40%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(b) Graph the cost equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-10%2C10%2C-10%2C50%2C10x%2B40%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-10%2C10%2C-10%2C50%2C10x%2B40%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(c) The revenue generated from the sale of x items is given by R = 50x. Graph the revenue equation on the same set of axes as the cost equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-10%2C10%2C-10%2C60%2C10x%2B40%2C50x%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-10%2C10%2C-10%2C60%2C10x%2B40%2C50x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(d) How many items must be produced for the revenue to equal the cost (the break-even point)?  The lines intersect at (1,50), therefore the number of items that must be produced to break even is x=1.<BR>\n" );
document.write( "You could have found this algebraically by letting C=R<BR>\n" );
document.write( "10x+40=50x<BR>\n" );
document.write( "10x-10x+40=50x-10x<BR>\n" );
document.write( "40=40x<BR>\n" );
document.write( "40/40=40x/40<BR>\n" );
document.write( "1=x<BR>\n" );
document.write( "Happy Calculating!!! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );