document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=398034>Question 398034</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A semiconductor manufacturer seeks to maximize its profits.  Testing indicates that they can produce 100,000 chips per week at a cost of $40 per chip, and sell them for $65 per chip.  They also find that they can produce 125,000 chips per week at a cost of $35 per chip, and sell them for $63 per chip.  How much profit can they expect to earn if they produce 130,000 chips per week?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #282053 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=282053\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Testing indicates that they can produce 100,000 chips per week at a cost of $40 per chip, and sell them for $65 per chip. They also find that they can produce 125,000 chips per week at a cost of $35 per chip, and sell them for $63 per chip. How much profit can they expect to earn if they produce 130,000 chips per week?<BR>\n" );
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document.write( "You have two points relating production and profit:<BR>\n" );
document.write( " (100000,25) and (125000,28)<BR>\n" );
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document.write( "slope = (28-25)/(125k-100k) = 3/25k = 0.00012<BR>\n" );
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document.write( "Form: y = mx+b<BR>\n" );
document.write( "25 = (0.00012)(10000) + b<BR>\n" );
document.write( "25 = 33+b<BR>\n" );
document.write( "b = -8<BR>\n" );
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document.write( "Equation:<BR>\n" );
document.write( "f(x) = (0.00012)x-8<BR>\n" );
document.write( "How much profit can they expect to earn if <BR>\n" );
document.write( "they produce 130,000 chips per week?<BR>\n" );
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document.write( "f(130000) = (0.00012)(130000) - 8<BR>\n" );
document.write( "f(130000) = 15.6-8 = $7.60<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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