document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1096406>Question 1096406</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The number of pounds of apples a cannery can produce and the processing cost are P(h) = 375h and C(n) = 0.35n + 1000 where P(h) is the number of pounds of apples that can be processed in h hours and C(n) is the cost of processing n pounds of apples.  Use composition of functions to find the cost of operating the cannery 32 hours\r<BR>\n" );
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document.write( "Please help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #710873 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=710873\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\">\r<BR>\n" );
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document.write( "The equation P(h) = 375h represents the number of pounds of apples that the cannery can produce. \r<BR>\n" );
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document.write( "Saying 375h is the same as 375*h which means \"375 times h\"\r<BR>\n" );
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document.write( "The basic idea is that h represents the placeholder for any positive real number. For example, if h = 2, then 2 hours pass by and 375*h = 375*2 = 750 pounds of apples are processed.\r<BR>\n" );
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document.write( "We can replace the P in P(h) = 375h with n to get n(h) = 375h. The n matches with the n in the other equation C(n) = 0.35n + 1000\r<BR>\n" );
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document.write( "Saying n(h) = 375h is the same as n = 375h\r<BR>\n" );
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document.write( "Since n = 375h, we can replace every copy of n in the second equation with 375h\r<BR>\n" );
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document.write( "C(n) = 0.35n + 1000\r<BR>\n" );
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document.write( "C(n) = 0.35*n + 1000\r<BR>\n" );
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document.write( "C(n) = 0.35*(n) + 1000\r<BR>\n" );
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document.write( "C(<font color=red>n</font>) = 0.35*(<font color=red>n</font>) + 1000\r<BR>\n" );
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document.write( "C(<font color=red>375h</font>) = 0.35*(<font color=red>375h</font>) + 1000 ... note how the n terms have been replaced with 375h\r<BR>\n" );
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document.write( "C(<font color=red>P(h)</font>) = 0.35*(375*h) + 1000 ... note how the 375h on the left side is replaced with P(h)\r<BR>\n" );
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document.write( "C(P(h)) = 0.35*(375*h) + 1000\r<BR>\n" );
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document.write( "C(P(h)) = (0.35*375)*h + 1000\r<BR>\n" );
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document.write( "C(P(h)) = 131.25*h + 1000\r<BR>\n" );
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document.write( "Now plug in h = 32 \r<BR>\n" );
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document.write( "C(P(h)) = 131.25*h + 1000\r<BR>\n" );
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document.write( "C(P(<font color=red>h</font>)) = 131.25*<font color=red>h</font> + 1000\r<BR>\n" );
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document.write( "C(P(<font color=red>32</font>)) = 131.25*<font color=red>32</font> + 1000 ... every h is replaced with 32\r<BR>\n" );
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document.write( "C(P(32)) = 131.25*32 + 1000\r<BR>\n" );
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document.write( "C(P(32)) = 4200 + 1000\r<BR>\n" );
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document.write( "C(P(32)) = 5200\r<BR>\n" );
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document.write( "Therefore the final answer is 5200 meaning that the total operating cost is $5,200 if you run the cannery for 32 hours.\r<BR>\n" );
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