document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=83171>Question 83171</A>: <I><SPAN STYLE=\"word-break: break-all;\"> #24<BR>\n" );
document.write( "Marginal Cost of Coffee The manager of a restaurant<BR>\n" );
document.write( "found that the cost to produce 100 cups of coffee is<BR>\n" );
document.write( "$11.02, while the cost to produce 400 cups is $40.12.<BR>\n" );
document.write( "Assume the cost is a linear function of x, the number<BR>\n" );
document.write( "of cups produced.<BR>\n" );
document.write( "a. Find a formula for C(x).<BR>\n" );
document.write( "b. What is the fixed cost?<BR>\n" );
document.write( "c. Find the total cost of producing 1000 cups.<BR>\n" );
document.write( "d. Find the total cost of producing 1001 cups.<BR>\n" );
document.write( "e. Find the marginal cost of the 1001st cup.<BR>\n" );
document.write( "f. What is the marginal cost of any cup and what does this<BR>\n" );
document.write( "mean to the manager?\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #59683 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=59683\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The manager of a restaurant found that the cost to produce <BR>\n" );
document.write( "100 cups of coffee is $11.02, <BR>\n" );
document.write( "while the cost to produce 400 cups is $40.12.<BR>\n" );
document.write( "Assume the cost is a linear function of x, the number of cups produced.<BR>\n" );
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document.write( "You have two points: (100,11.02) and (400,40.12)<BR>\n" );
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document.write( "a. Find a formula for C(x).<BR>\n" );
document.write( "slope - [40.12-11.02]/[400-300] = 29.10/300 = 0.097..<BR>\n" );
document.write( "Form is y=mx+b where y=31.02 when x=100 and m=0.097...<BR>\n" );
document.write( "31.02 = 0.097(100)+b<BR>\n" );
document.write( "31.02 = 9.7 + b<BR>\n" );
document.write( "b= 21.32<BR>\n" );
document.write( "EQUATION:<BR>\n" );
document.write( "Cost(x) = 0.097x + 21.32 <BR>\n" );
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document.write( "b. What is the fixed cost? $21.32<BR>\n" );
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document.write( "c. Find the total cost of producing 1000 cups.<BR>\n" );
document.write( "C(1000) = 0.097(1000)+21.32 = $118.32<BR>\n" );
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document.write( "d. Find the total cost of producing 1001 cups.<BR>\n" );
document.write( "Add 9.7 cents the the cost of part c.<BR>\n" );
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document.write( "e. Find the marginal cost of the 1001st cup.<BR>\n" );
document.write( "The slope is the marginal cost: 9.7 cents<BR>\n" );
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document.write( "f. What is the marginal cost of any cup and what does this<BR>\n" );
document.write( "mean to the manager?<BR>\n" );
document.write( "The marginal cost for any cup is 9.7 cents.<BR>\n" );
document.write( "If he produces no cups his overhead is $21.32<BR>\n" );
document.write( "For each cup he sells he gains 9.7 cents.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );