document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=70361>Question 70361</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The inventor of a new product believes that the cost of producing the product is given by the function: C(x)= 1.75x + 7000\r<BR>\n" );
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document.write( "The cost of 2000 units of her invention is $10,500.\r<BR>\n" );
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document.write( "If the inventor charges $4 per unit, then her profit for producing and selling x units is given by the function: P(x)= 2.25x - 7000\r<BR>\n" );
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document.write( "(a) What is her profit if she sells 2000 units?<BR>\n" );
document.write( "(b) What is her profit if she sells 5000 units?<BR>\n" );
document.write( "(c) What is the break-even point for sales? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #50192 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=50192\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> From the way this problem is worded, the equation for C(x) is not needed to answer the questions<BR>\n" );
document.write( "that are asked.  The only equation that applies is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+2.25x+-+7000 ALIGN=MIDDLE  ALT=\"P%28x%29+=+2.25x+-+7000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The first question ... What is the profit if she sells 2000 units?  Calculate the profit by<BR>\n" );
document.write( "setting x equal to 2000 units so that the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+%282.25%29%2A%282000%29+-+7000+=+4500+-+7000+=+-2500 ALIGN=MIDDLE  ALT=\"P%28x%29+=+%282.25%29%2A%282000%29+-+7000+=+4500+-+7000+=+-2500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The negative sign tells you that overall she loses $2500 if she sells only 2000 units.<BR>\n" );
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document.write( "The second question ... What is the profit if she sells 5000 units?  Do the same calculation<BR>\n" );
document.write( "as above, but this time set x equal to 5000 units so that the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+%282.25%29%2A%285000%29+-+7000+=+11250+-+7000+=+4250 ALIGN=MIDDLE  ALT=\"P%28x%29+=+%282.25%29%2A%285000%29+-+7000+=+11250+-+7000+=+4250\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The positive answer tells you that overall she makes $4,250 if she sells 5000 units.<BR>\n" );
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document.write( "So somewhere between sales of 2000 units (a loss) and selling 5000 units (a gain) she<BR>\n" );
document.write( "reach a break-even point.  At that break-even point her profit would be zero (neither a<BR>\n" );
document.write( "loss nor a gain).  So this time set the profit equal to zero in the equation and solve the<BR>\n" );
document.write( "resulting equation for x.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+%282.25%29%2Ax+-+7000 ALIGN=MIDDLE  ALT=\"0+=+%282.25%29%2Ax+-+7000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Add 7000 to both sides and transpose the equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.25%2Ax+=+7000 ALIGN=MIDDLE  ALT=\"2.25%2Ax+=+7000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Divide both sides by 2.25 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+7000%2F2.25+=+3111.11 ALIGN=MIDDLE  ALT=\"x+=+7000%2F2.25+=+3111.11\"   DISABLED_style= \"max-width:90%; height:auto;\" >}<BR>\n" );
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document.write( "This result tells you that if she sells less than this amount she loses money, but if<BR>\n" );
document.write( "she sells more than this number of units she makes money.  Therefore, you can say that<BR>\n" );
document.write( "she loses a very small amount of money if she sells 3111 units, and she makes a very small<BR>\n" );
document.write( "amount of money if she sells 3112 units.<BR>\n" );
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document.write( "Hope this helps you to see your way through the problem ... especially with regarding<BR>\n" );
document.write( "the information on the costs involved with production, C(x), and the sales price of $4.00<BR>\n" );
document.write( "per unit. That information was not needed because you were provided with an<BR>\n" );
document.write( "equation that <BR>\n" );
document.write( "directly calculates profit based on the number of units sold. </SPAN>\n" );
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