document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=466677>Question 466677</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can Someone please help me with this question <BR>\n" );
document.write( "The revenue, R, generated by selling games with a particular price is given by R(p) = –15p2 + 300 p + 1200. Graph the revenue function without a <BR>\n" );
document.write( "calculator and find the price that<BR>\n" );
document.write( "will yield the maximum revenue. What is the maximum revenue? Explain<BR>\n" );
document.write( "in real world terms why this graph is parabolic. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #319969 by </B><A HREF=/tutors/aboutme.mpl?userid=ccs2011><B>ccs2011(207)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ccs2011><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=ccs2011><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=319969\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Revenue = price*quantity<BR>\n" );
document.write( "Typically the higher the price the less likely someone will buy the product<BR>\n" );
document.write( "Or in other words there is less demand<BR>\n" );
document.write( "At a low price, quantity may be high but overall revenue will be low<BR>\n" );
document.write( "As price increases, revenue increases <BR>\n" );
document.write( "However, at some point the price will increase too much such that the quantity becomes too low and the overall revenue will start decreasing<BR>\n" );
document.write( "This is the optimal price for maximum revenue.<BR>\n" );
document.write( "At a very high price, quantity will be very low and revenue will be low as well<BR>\n" );
document.write( "Thus the inverse relationship between price and quantity yields a parabolic revenue curve.<BR>\n" );
document.write( "To find maximum, determine vertex of the graph.<BR>\n" );
document.write( "Given quadratic equation of the form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the x_coordinate of the vertex or line of symmetry is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-b%2F2a ALIGN=MIDDLE  ALT=\"x+=+-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For our revenue function:<BR>\n" );
document.write( "a = -15<BR>\n" );
document.write( "b = 300<BR>\n" );
document.write( "c = 1200<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-300%29%2F%282%2A-15%29 ALIGN=MIDDLE  ALT=\"x+=+%28-300%29%2F%282%2A-15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-300%29%2F-30 ALIGN=MIDDLE  ALT=\"x+=+%28-300%29%2F-30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+10 ALIGN=MIDDLE  ALT=\"x+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To find y_coordinate, substitute 10 into function<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-15%2810%5E2%29+%2B+300%2810%29+%2B+1200 ALIGN=MIDDLE  ALT=\"y+=+-15%2810%5E2%29+%2B+300%2810%29+%2B+1200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-1500+%2B+3000+%2B1200 ALIGN=MIDDLE  ALT=\"y+=+-1500+%2B+3000+%2B1200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2700 ALIGN=MIDDLE  ALT=\"y+=+2700\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Vertex is at (10, 2700)<BR>\n" );
document.write( "Thus max revenue is $2700 at a price of $10 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );