document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=854264>Question 854264</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Someone kindly provide solutio to this....thankss\r<BR>\n" );
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document.write( "assume that a firm knows that the cost to make x items is given by the cost function C(x) = 6xsquare + 700x dollars. it also knows that the revenue from x items is given by the revenue function R(x) = 1000x + 400. \r<BR>\n" );
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document.write( "Required:<BR>\n" );
document.write( "Maximum profit they can expectt and how many of these items they have to produce and sell to make this maximum profitt. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #514562 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=514562\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> c(x) = 6x^2 + 700x<BR>\n" );
document.write( "r(x) = 1000x + 400\r<BR>\n" );
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document.write( "profit is equal to p(x) which is equal to r(x) - c(x)\r<BR>\n" );
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document.write( "this becomes:\r<BR>\n" );
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document.write( "p(x) = 1000x + 400 - (6x^2 + 700x)\r<BR>\n" );
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document.write( "simplify this to get:\r<BR>\n" );
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document.write( "p(x) = 1000x + 400 - 6x^2 - 700x\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "p(x) = 300x + 400 - 6x^2\r<BR>\n" );
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document.write( "reorder the terms to the largest exponent is on the left to get:\r<BR>\n" );
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document.write( "p(x) = -6x^2 + 300x + 400\r<BR>\n" );
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document.write( "set p(x) = 0 to get:\r<BR>\n" );
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document.write( "-6x^2 + 300x + 400 = 0\r<BR>\n" );
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document.write( "since this is a quadratic equation in standard form, then the max/min point will be at:\r<BR>\n" );
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document.write( "(x,y) = (-b/2a,f(-b/2a)\r<BR>\n" );
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document.write( "a = -6<BR>\n" );
document.write( "b = 300<BR>\n" );
document.write( "c = 400\r<BR>\n" );
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document.write( "-b/2a = -300 / -12 = 300/12 = 25\r<BR>\n" );
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document.write( "f(-b/2a) = f(25) = -6(25)^2 + 300(25) + 400 which is equal to 4150.\r<BR>\n" );
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document.write( "maximum profit should be equal to 4150 dollars.\r<BR>\n" );
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document.write( "you can graph the equation of p(x) = -6x^2 + 300x + 400.<BR>\n" );
document.write( "that graph is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C60%2C-100%2C5000%2C-6x%5E2+%2B+300x+%2B+400%2C4150%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-10%2C60%2C-100%2C5000%2C-6x%5E2+%2B+300x+%2B+400%2C4150%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "i put a horizontal line at y = 4150 to show you that it is at the max point of the graph.\r<BR>\n" );
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document.write( "the profit formula is a quadratic equation.\r<BR>\n" );
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document.write( "you had c(x) and you had r(x).\r<BR>\n" );
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document.write( "you needed to calculate p(x) = r(x) - c(x) and then solve for the maximum point 0of that equation as was done above.\r<BR>\n" );
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