document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=459478>Question 459478</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Melinda and JP are selling lemonade at a stand in her front yard.  The linear expression below models her total profit in dollars after h hours.<BR>\n" );
document.write( "2<BR>\n" );
document.write( "-(6h-5)+4h<BR>\n" );
document.write( "3\r<BR>\n" );
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document.write( "How much does her profit increase each hour?  Explain in words and worked out expressions.\r<BR>\n" );
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document.write( "Also,\r<BR>\n" );
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document.write( "Evaluate the expression for h = 0.  wHAT DOES THIS VALUE MEAN IN THE CONTEXT OF THE PROBLEM?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #315092 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=315092\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "First, distribute the fraction.  Second, collect like terms.  The change in profit per hour will be the coefficient on <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large h\">.  If this coefficient is a positive number, then the change is an increase.  If the coefficient is a negative number, then the change represents a loss.\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large h\"> is zero, then you are calculating the profit when she first starts.  You would expect this to be a negative number because it costs something to start any enterprise.  So the value of the expression is the amount of money that it cost to set up the stand, make the first batch of lemonade, buy cups, etc.\r<BR>\n" );
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document.write( "Note that this model fails as soon as the business has to replenish consumable items, such as lemons, sugar, paper cups, or even dish soap if the cups are washable rather than disposable.  As soon as more expenditures are made, the constant term of the equation has to change to reflect the total cost of running the business.\r<BR>\n" );
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document.write( "And, by the way, don't type in ALL CAPS.  That is the text equivalent of shouting and is both annoying and rude.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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