document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=242803>Question 242803</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Joanne sells silk-screened T-shirts at community festivals and craft fairs. Her marginal cost to produce one t-shirt is $450. Her total cost to produce 80 t-shirts is $420, and she sells them for $8 each.<BR>\n" );
document.write( "a) find the linear cost function for joanne's t-shirt production<BR>\n" );
document.write( "b) How many t-shirts must she produce and sell in order to break even?<BR>\n" );
document.write( "c) How many t-shirts must she produce and sell to make a profit of $900?\r<BR>\n" );
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document.write( "I need to know how to do it step by step, if anyone can help!! Thank you so much </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #177769 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=177769\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, define your terms. <BR>\n" );
document.write( "MC = marginal cost to make 1 t=shirt, which has to be $4.50 (not $450).<BR>\n" );
document.write( "The cost to print 80 shirts is 420.<BR>\n" );
document.write( "80*4.5 = 360, so there is an additional cost of $60.<BR>\n" );
document.write( "Since this is not a marginal cost, it must be a fixed cost.<BR>\n" );
document.write( "Recall that Total Cost = Fixed Cost + (Marginal Cost * Number of items produced)<BR>\n" );
document.write( "TC = FC + MC(X), where X is the number of items<BR>\n" );
document.write( "TC = 60 + 4.5X  (the answer to part a, the cost function)<BR>\n" );
document.write( "Now we should note that $8 is the Price that she charges buyers.<BR>\n" );
document.write( "P = 8<BR>\n" );
document.write( "Profit = P*X -TC = 8X - 60 - 4.5X<BR>\n" );
document.write( "Break even is the point where Profit = 0.<BR>\n" );
document.write( "0 = 8X - 60 - 4.5X<BR>\n" );
document.write( "Add 60 to both sided<BR>\n" );
document.write( "60 = 8X - 4.5X = 3.5X<BR>\n" );
document.write( "Dividing by 3.5<BR>\n" );
document.write( "60/3.5 = X = 17 and a fraction, so she has to sell 18 shirts.<BR>\n" );
document.write( "18 * 8 = 144 total revenue<BR>\n" );
document.write( "60 + 4.5*18 = 141 total cost<BR>\n" );
document.write( "So that's very close to break even.  Close enough.<BR>\n" );
document.write( "Continuing with the question of $900 profit...<BR>\n" );
document.write( "900 = 8X - 60 - 4.5X  (by substituting back into the equation)<BR>\n" );
document.write( "Adding 60 to both sides:<BR>\n" );
document.write( "960 = 3.5X<BR>\n" );
document.write( "Dividing by 3.5.<BR>\n" );
document.write( "274 (and a fraction) = X<BR>\n" );
document.write( "Therefore, we propose that when she sells 274 shirts, she earns $900 profit.<BR>\n" );
document.write( "Check your work!<BR>\n" );
document.write( "Profit = Total Revenue - Total Cost<BR>\n" );
document.write( "Profit = $8 per shirt * 274 shirts - $60 fixed cost - $4.50 * 274 shirts<BR>\n" );
document.write( "Profit = 2192 - 60 - 1233<BR>\n" );
document.write( "Profit = 2192 - 1293 = 899<BR>\n" );
document.write( "That checks as close as we can get it.<BR>\n" );
document.write( "Why did I ignore the fractions?<BR>\n" );
document.write( "You cannot sell a fraction of a shirt.\r<BR>\n" );
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