document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1167022>Question 1167022</A>: <I><SPAN STYLE=\"word-break: break-all;\"> im sory didnt realize i didnt include the actual function here it is. \r<BR>\n" );
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document.write( "For a certain company, the cost function for producing x items is C(x)=30x+250 and the revenue function for selling x items is R(x)=−0.5(x−110)2+6,050. The maximum capacity of the company is 140 items.\r<BR>\n" );
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document.write( "The profit function P(x) is the revenue function R(x) (how much it takes in) minus the cost function C(x) (how much it spends). In economic models, one typically assumes that a company wants to maximize its profit, or at least make a profit!\r<BR>\n" );
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document.write( "Answers to some of the questions are given below so that you can check your work.\r<BR>\n" );
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document.write( "Assuming that the company sells all that it produces, what is the profit function?<BR>\n" );
document.write( "P(x)=\r<BR>\n" );
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document.write( "Hint: Profit = Revenue - Cost as we examined in Discussion 3.<BR>\n" );
document.write( "What is the domain of P(x)?<BR>\n" );
document.write( "Hint: Does calculating P(x) make sense when x=−10 or x=1,000?<BR>\n" );
document.write( "The company can choose to produce either 80 or 90 items. What is their profit for each case, and which level of production should they choose?<BR>\n" );
document.write( "Profit when producing 80 items =\r<BR>\n" );
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document.write( "Profit when producing 90 items =\r<BR>\n" );
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document.write( "Can you explain, from our model, why the company makes less profit when producing 10 more units? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #791606 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=791606\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> −0.5(x−110)^2+6,050-(30x+250) is the profit function<BR>\n" );
document.write( "This is -0.5(x^2-220x+12100)+6050-30x-250<BR>\n" );
document.write( "or -0.5x^2+110x-6050+6050-30x-250<BR>\n" );
document.write( "or -0.5x^2+80x-250<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-40%2C200%2C-500%2C3000%2C-0.5x%5E2%2B80x-250%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-40%2C200%2C-500%2C3000%2C-0.5x%5E2%2B80x-250%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The domain is all x but -units make no sense and 1000 units is a large loss.<BR>\n" );
document.write( "At 80 units the profit is -3200+6400-250 or $2950<BR>\n" );
document.write( "at 90 units it is $2800<BR>\n" );
document.write( "The maximum is when x=-b/2a or -80/-1 or 80 units.\r<BR>\n" );
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document.write( "With squared functions as production (in this instance) increases, there could be decreasing revenue simply because the company may oversupply and have to either store or sell at a lower price.  This is an economics question rather than a math question. </SPAN>\n" );
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