document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=83991>Question 83991</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please show me the way.. A restaurant determined that it's monthly cost function is given by C=3000=16q, where q is the number of dinners sold per month. q=1200-20p, where p is the price of the dinner. <BR>\n" );
document.write( "a) Solve for p in terms of q and write the revenue and profit as a function of q<BR>\n" );
document.write( "b) Find the break even point in terms of q. (the min and max # dinners/mo it can serve without losing $)<BR>\n" );
document.write( "c) Write the cost, revenue and profit as functions of p and find breakeven points in terms of p.<BR>\n" );
document.write( "d) Determin range of prices for which the restaurant make a profit.<BR>\n" );
document.write( "I know this is alot, but I am lost. Any help is appreciated. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #60469 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=60469\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  A restaurant determined that it's monthly cost function is given by C=3000=16q, where q is the number of dinners sold per month. <BR>\n" );
document.write( "q = 1200-20p, where p is the price of the dinner.<BR>\n" );
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document.write( "a) Solve for p in terms of q and write the revenue and profit as a function of q<BR>\n" );
document.write( "q = 1200-20p<BR>\n" );
document.write( "+20p = 1200 - q<BR>\n" );
document.write( "p = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281200-q%29%29%2F20 ALIGN=MIDDLE  ALT=\"%28%281200-q%29%29%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Revenue = p * q; substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281200-q%29%29%2F20 ALIGN=MIDDLE  ALT=\"%28%281200-q%29%29%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" > for p:\r<BR>\n" );
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document.write( "Rev = q(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281200-q%29%29%2F20 ALIGN=MIDDLE  ALT=\"%28%281200-q%29%29%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "Rev = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281200q+-+q%5E2%29%29%2F20 ALIGN=MIDDLE  ALT=\"%28%281200q+-+q%5E2%29%29%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Rev = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2860q+-+.05q%5E2%29 ALIGN=MIDDLE  ALT=\"%2860q+-+.05q%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >; divide both terms by 20<BR>\n" );
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document.write( "Profit = Rev - Cost<BR>\n" );
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document.write( "Profit = (60q - .05q^2) - (3000 + 16q)<BR>\n" );
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document.write( "Profit = 60q - .05q^2 - 3000 - 16q<BR>\n" );
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document.write( "Profit = -.05q^2 + 44q - 3000<BR>\n" );
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document.write( "b) Find the break even point in terms of q. (the min and max # dinners/mo it can serve without losing $)<BR>\n" );
document.write( "Breakeven point is when profit = 0<BR>\n" );
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document.write( "-.05q^2 + 44q - 3000 = 0<BR>\n" );
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document.write( "Using the quadratic formula, I got:<BR>\n" );
document.write( "q ~ 75 meals min and q ~ 805 max, to not lose money<BR>\n" );
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document.write( "Graph this equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-200%2C+1000%2C+-1000%2C+8000%2C+-.05x%5E2+%2B+44x+-+3000%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-200%2C+1000%2C+-1000%2C+8000%2C+-.05x%5E2+%2B+44x+-+3000%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Profit on the vertical and number of meals on the horizontal<BR>\n" );
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document.write( "c) Write the cost, revenue and profit as functions of p and find breakeven points in terms of p.<BR>\n" );
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document.write( "Cost = 3000 + 16q<BR>\n" );
document.write( "q = 1200-20p<BR>\n" );
document.write( "Replace q with (1200-20p)<BR>\n" );
document.write( "Cost = 3000 + 16(1200- 20p)<BR>\n" );
document.write( "Cost = 3000 + 19200 - 320p<BR>\n" );
document.write( "Cost = 22200 -320p<BR>\n" );
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document.write( "Revenue = p * q<BR>\n" );
document.write( "Replace q with (1200-20p)<BR>\n" );
document.write( "Rev = p(1200-20p)<BR>\n" );
document.write( "Rev = 1200p - 20p^2<BR>\n" );
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document.write( "Profit = Revenue - Cost<BR>\n" );
document.write( "Profit = 1200p - 20p^2 - (22200 - 320p)<BR>\n" );
document.write( "Profit = 1200p - 20p^2 - 22200 + 320p<BR>\n" );
document.write( "Profit = -20p^2 + 1520p - 21000<BR>\n" );
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document.write( "Breakeven is when profit = 0<BR>\n" );
document.write( "-20p^2+ 1520p - 21000 = 0<BR>\n" );
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document.write( "d) Determine range of prices for which the restaurant make a profit.<BR>\n" );
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document.write( "Solve for p in the above equation: I got p = 18.93 and p = 57.85<BR>\n" );
document.write( "Profit between these two values<BR>\n" );
document.write( "Graph would look like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-10%2C+70%2C+-1000%2C+8000%2C+-20x%5E2%2B+1520x+-+21000+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-10%2C+70%2C+-1000%2C+8000%2C+-20x%5E2%2B+1520x+-+21000+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Profit on the vertical and meal price on the horizonal<BR>\n" );
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document.write( "A lot of chance for error here, check my calculations.\r<BR>\n" );
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