document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1163385>Question 1163385</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The supply function qs = f (p) for a product is quadratic. Three points which lie on the supply function are (60, 2750), (70, 6000) and (80, 9750).\r<BR>\n" );
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document.write( "a)	 Determine the equation for the supply function<BR>\n" );
document.write( "b)	Make any observation you can about the restricted domain of the function<BR>\n" );
document.write( "c)	Compute and interpret the p intercept.<BR>\n" );
document.write( "d)	What quantity will be supplied at a price of $75<BR>\n" );
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document.write( "The function is quadratic:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q%28p%29+=+ap%5E2%2Bbp%2Bc ALIGN=MIDDLE  ALT=\"q%28p%29+=+ap%5E2%2Bbp%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Use the three given points to form three equations in the unknowns a, b, and c.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3600a%2B60b%2Bc+=+2750 ALIGN=MIDDLE  ALT=\"3600a%2B60b%2Bc+=+2750\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4900a%2B70b%2Bc+=+6000 ALIGN=MIDDLE  ALT=\"4900a%2B70b%2Bc+=+6000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6400a%2B80b%2Bc+=+9750 ALIGN=MIDDLE  ALT=\"6400a%2B80b%2Bc+=+9750\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Eliminate c between the first and second equations, and between the second and third:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1300a%2B10b+=+3250 ALIGN=MIDDLE  ALT=\"1300a%2B10b+=+3250\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1500a%2B10b+=+3750 ALIGN=MIDDLE  ALT=\"1500a%2B10b+=+3750\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Eliminate b between those two equations:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200a+=+500 ALIGN=MIDDLE  ALT=\"200a+=+500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+2.5 ALIGN=MIDDLE  ALT=\"a+=+2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Plug a=2.5 in either of the previous two equations to find b=0.<br><BR>\n" );
document.write( "Plug a=2.5 and b=0 in any of the original equations to find a=-6250.<br><BR>\n" );
document.write( "a) ANSWER: The supply function is f(p) = 2.5p^2-6250<br><BR>\n" );
document.write( "b) Mathematically, a negative price doesn't make sense -- so the restriction on the domain is p greater than or equal to 0.<br><BR>\n" );
document.write( "But realistically a negative quantity supplied doesn't make sense either.  f(50)=0, so realistically the restriction on the domain is p greater than or equal to 50.<br><BR>\n" );
document.write( "c) The p-intercept is when q=0, which is (50,0).  That means no products will be supplied when the price is $50.<br><BR>\n" );
document.write( "d) q(75) = 7812.5.  I'm not sure whether in the real world you would mean the quantity supplied at a price of $75 is 7812 or 7813....<br><BR>\n" );
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