document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=164277>Question 164277</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Question: Write a cost function for the problem. Assume that the relationship is linear. \r<BR>\n" );
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document.write( "Marginal cost, $40; 70 items cost $3800 to produce<BR>\n" );
document.write( "a) C(x)=14x+3800<BR>\n" );
document.write( "b) C(x)=40x+1000<BR>\n" );
document.write( "c) C(x)=40x+3800<BR>\n" );
document.write( "d) C(x)=14x+100\r<BR>\n" );
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document.write( "Question: Assume that the sales of a certain appliance dealer are approximated by a linear function. Suppose that sales were $10,500 in 1982 and $67,000 in 1987. Let x=0 represent 1982. Find the equation giving yearly sales S(x).\r<BR>\n" );
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document.write( "a) S(x)=11,300x+67,000<BR>\n" );
document.write( "b) S(x)=56,500x+10,500<BR>\n" );
document.write( "c) S(x)=56,500x+67,000<BR>\n" );
document.write( "d) S(x)=11,300x+10,500\r<BR>\n" );
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document.write( "Mike </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #121038 by </B><A HREF=/tutors/aboutme.mpl?userid=watchmath><B>watchmath(2)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=watchmath><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=121038\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Marginal cost means additional cost for additional item which is $40/item. But this is exactly the slope. You have another information that (70, 3800) is on the line.<BR>\n" );
document.write( "So by the point slope formula <BR>\n" );
document.write( "y-y_1=m(x-x_1)<BR>\n" );
document.write( "we have<BR>\n" );
document.write( "C-3800= 40(x-70)<BR>\n" );
document.write( "C(x)=40(x-70)+3800<BR>\n" );
document.write( "C(x)=40x +1000<BR>\n" );
document.write( "So the answer ============> (b)\r<BR>\n" );
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document.write( "The given two data about the sales in 1982 and 1987 tell us that the point<BR>\n" );
document.write( "(1982, 10,500) and (1987, 67,000) are on the line.<BR>\n" );
document.write( "The slope then equals (67,000 - 10,500)/(1987 - 1982) =56,500/5=11300.<BR>\n" );
document.write( "We have<BR>\n" );
document.write( "S(x)=11,300 x+b<BR>\n" );
document.write( "since x=0 correspond to 1982 and we now that S=10,500 in 1982 then<BR>\n" );
document.write( "10,500 =11,300 (0)+b ========> b=10,500 and therefore<BR>\n" );
document.write( "S(x)=11,300x+ 10,500.\r<BR>\n" );
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document.write( "More Help?<BR>\n" );
document.write( "Visit http://www.watchmath.com </SPAN>\n" );
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