document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201982>Question 1201982</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the cost of making x thousand pretzels per week is c=.4x^2-28x+87 and the revenue from selling x thousand pretzels per week is r=-.6x^2+8x find the equation for profit where (p=r-c) C and R are in thousands of dollars </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #836591 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=836591\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer: <font color=red size=4>P = -x^2 + 36x - 87</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Work Shown:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Profit = Revenue - Cost<BR>\n" );
document.write( "P = R - C<BR>\n" );
document.write( "P = (-0.6x^2 + 8x) - (0.4x^2 - 28x + 87)<BR>\n" );
document.write( "P = -0.6x^2 + 8x - 0.4x^2 + 28x - 87<BR>\n" );
document.write( "P = (-0.6x^2-0.4x^2) + (8x+28x) - 87<BR>\n" );
document.write( "P = -x^2 + 36x - 87\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "----------------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "Edit: The student requested finding the vertex.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "There are few ways to find the vertex. One way is to note that the parabola y = -x^2+36x-87 is of the form y = ax^2+bx+c<BR>\n" );
document.write( "a = -1<BR>\n" );
document.write( "b = 36<BR>\n" );
document.write( "c = -87\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The vertex is of the form (h,k)<BR>\n" );
document.write( "The steps to calculate h would be:<BR>\n" );
document.write( "h = -b/(2a)<BR>\n" );
document.write( "h = -36/(2*(-1))<BR>\n" );
document.write( "h = -36/(-2)<BR>\n" );
document.write( "h = 18<BR>\n" );
document.write( "This is the x coordinate of the vertex.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Plug that into the function to find its paired y coordinate.<BR>\n" );
document.write( "y = -x^2+36x-87<BR>\n" );
document.write( "y = -18^2+36(18)-87<BR>\n" );
document.write( "y = 237<BR>\n" );
document.write( "The vertex is located at (h,k) = <font color=red>(18, 237)</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "It means that <font color=red>selling 18 thousand pretzels will bring in a max profit of 237 thousand dollars.</font><BR>\n" );
document.write( "The point (18, 237) is the highest point on the parabola.<BR>\n" );
document.write( "I recommend using a graphing app such as Desmos or GeoGebra to confirm the answer is correct. <BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );