document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=993902>Question 993902</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A manufacturer has 2900 units in stock. The product is now selling at $8 per unit. Next month the unit price will increase by $0.50. The manufacturer wants the total revenue received from the sale of the 2900 units to be no less than $23750. What is the number of units that can be sold this month? <BR>\n" );
document.write( "At most _______ units </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #613193 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=613193\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if he sold all 2900 at 8 dollars each, he would get 23200 total.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's 550 short of his goal of at least 23750.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the difference in price between 8 and 8.50 is .50.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "take the 550 and divide it by .50 and you get 1100.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "he would need to sell a minimum of 1100 units at 8.50.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2900 - 1100 = 1800.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "he would therefore sell 1800 at 8.00 and 1100 at 8.50 and he would get 8 * 1800 = 14,400 + 8.50 * 1100 = 9,350 for a total orf 23,750.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can also solve this algebraically as follows:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = number of units sold at 8 dollars each.<BR>\n" );
document.write( "y = number of units sold at 8.5 dollars each.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "first equation is x + y = 2900<BR>\n" );
document.write( "second equation is 8x + 8.5y >= 23750\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "from the first equation, solve for y to get y = 2900 - x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "replace y with 2900 - x in the second equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "8x + 8.5 * (2900-x) >= 23750\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "8x + 24650 - 8.5x >= 23750\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "subtract 8x from both sides of this equation and subtract 23750 from both sides of this equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "24650 - 23750 = 8.5x - 8x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "900 = .5x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide both sides of this equation by 1.5 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = 1800.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since x + y = 2900, this means that y = 1100.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solution is x = 1800 and y = 1100\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x is the number sold at 8 dollars<BR>\n" );
document.write( "y is the number sold at 8.5 dollars\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "same answer as before when we used logic.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );