document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=473563>Question 473563</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can anyone help me with this? <BR>\n" );
document.write( "Suppose you own a strip mall. You want to determine the amount of rent you should charge to maximize your profit. The given equation measure the profit, P (is in thousands of dollars), per square foot of rental space (m is dollars per square foot).\r<BR>\n" );
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document.write( "   P(d) = -8.3m^2 + 53.1m - 26.5\r<BR>\n" );
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document.write( "1.	Does the graph of this equation open up or down? What algebraic information can you use to determine this? <BR>\n" );
document.write( "2.	Describe what happens to the profit as the rent per square foot is increased. Discuss the different amounts of profit defined by the graph and the equation. <BR>\n" );
document.write( "3.	Use the quadratic formula to determine the amounts that should be charged for rent that will give you zero profit. Round the value of m to the nearest tenth of a square foot. <BR>\n" );
document.write( "What do the solutions represent? Is there a solution that does not make sense? If so, in what ways does the solution not make sense? \r<BR>\n" );
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document.write( "4.	Will this equation give you a maximum profit or a minimum profit? How do you know? <BR>\n" );
document.write( "5.	What price should be charged to reach the maximum or minimum profit? <BR>\n" );
document.write( "6.	How much profit will you have at the peak or low? Remember that the profit is measured in thousands of dollars. Include the proper units. <BR>\n" );
document.write( "7.	What is the point of the vertex? Calculate this value. How does this number relate to your answers in numbers 5 and 6? <BR>\n" );
document.write( "8.	How many solutions are there to the equation ? How do you know? Give an algebraic and a written response. <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 #324810 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=324810\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose you own a strip mall. You want to determine the amount of rent you should charge to maximize your profit. The given equation measure the profit, P (is in thousands of dollars), per square foot of rental space (m is dollars per square foot). <BR>\n" );
document.write( "P(d) = -8.3m^2 + 53.1m - 26.5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C50%2C-10%2C150%2C-8.3x%5E2+%2B+53.1x+-+26.5%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C50%2C-10%2C150%2C-8.3x%5E2+%2B+53.1x+-+26.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "1. Does the graph of this equation open up or down? What algebraic information can you use to determine this?<BR>\n" );
document.write( "Ans: Opens down because the coefficient of x^2 is negative.<BR>\n" );
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document.write( "2. Describe what happens to the profit as the rent per square foot is increased. Profit rises then falls as square footage increases.<BR>\n" );
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document.write( "Discuss the different amounts of profit defined by the graph and the equation.<BR>\n" );
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document.write( "3. Use the quadratic formula to determine the amounts that should be charged for rent that will give you zero profit. Round the value of m to the nearest tenth of a square foot.<BR>\n" );
document.write( "Solve -8.3m^2 + 53.1m - 26.5 = 0<BR>\n" );
document.write( "m = 0.5456 ; m = 5.852<BR>\n" );
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document.write( "What do the solutions represent? Is there a solution that does not make sense? If so, in what ways does the solution not make sense?<BR>\n" );
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document.write( "4. Will this equation give you a maximum profit or a minimum profit? How do you know?<BR>\n" );
document.write( "Maximum because it has a peak.<BR>\n" );
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document.write( "5. What price should be charged to reach the maximum or minimum profit?<BR>\n" );
document.write( "m = -b/(2a) = -53.1/(2*-8.3) = 3.20<BR>\n" );
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document.write( "6. How much profit will you have at the peak or low? Remember that the profit is measured in thousands of dollars. Include the proper units.<BR>\n" );
document.write( "$58,428<BR>\n" );
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document.write( "7. What is the point of the vertex? Calculate this value. How does this number relate to your answers in numbers 5 and 6?<BR>\n" );
document.write( "They are the same<BR>\n" );
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document.write( "8. How many solutions are there to the equation ? How do you know? Give an algebraic and a written response.<BR>\n" );
document.write( "Two because the equation is a quadratic.<BR>\n" );
document.write( "The discriminant is positive so there are 2 Real Number solutions.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. \r<BR>\n" );
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