document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1153924>Question 1153924</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A manufacturing company makes two types of water skis, a trick ski and a slalom ski. The relevant manufacturing data are given in the table:\r<BR>\n" );
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document.write( "LABOR HRS<BR>\n" );
document.write( "                                                               MAX LABOR HRS AVAILABLE PER DAY<BR>\n" );
document.write( "DEPT	   Trick Ski  	Slalom Ski	<BR>\n" );
document.write( "Fabricating	8	            6                                  264<BR>\n" );
document.write( "Finishing	        1	            1	                                 40 \r<BR>\n" );
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document.write( "​(A) If the profit on a trick ski is ​$40 and the profit on a slalom ski is ​$50​, how many of each type of ski should be manufactured each day to realize a maximum​ profit? What is the maximum​ profit? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #776248 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=776248\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
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document.write( "<tr><TD ></TD><TD >Trick Ski</TD><TD >Slalom Ski</TD><TD >Max Labor Hrs Available Per Day</TD></tr>\r\n" );
document.write( "<tr><TD >Fabricating</TD><TD >8</TD><TD >6</TD><TD >264</TD></tr>\r\n" );
document.write( "<tr><TD >Finishing</TD><TD >1</TD><TD >1</TD><TD >40</TD></tr>\r\n" );
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document.write( "x = number of trick skis sold<BR>\n" );
document.write( "y = number of slalom skis sold<BR>\n" );
document.write( "both x and y are nonnegative, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E=+0 ALIGN=MIDDLE  ALT=\"x+%3E=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3E=+0 ALIGN=MIDDLE  ALT=\"y+%3E=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "From the first row of the table we see that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B6y+%3C=+264 ALIGN=MIDDLE  ALT=\"8x%2B6y+%3C=+264\"   DISABLED_style= \"max-width:90%; height:auto;\" > because the 8x represents the labor hours for making x number of trick skis, while 6y is the labor hours for making y number of slalom skis. The total (8x+6y) cannot exceed 264 hours, which is why we end up with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B6y+%3C=+264 ALIGN=MIDDLE  ALT=\"8x%2B6y+%3C=+264\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Through similar reasoning, the second row gives us this inequality: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By+%3C=+40 ALIGN=MIDDLE  ALT=\"x%2By+%3C=+40\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Graph the following system of inequalities<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%3E=0%2C+y%3E=0%2C+8x%2B6y%3C=264%2C+x%2By+%3C=40%29 ALIGN=MIDDLE  ALT=\"system%28x%3E=0%2C+y%3E=0%2C+8x%2B6y%3C=264%2C+x%2By+%3C=40%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "to get this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/IdBNIlh.png\"><BR>\n" );
document.write( "Let me know if you need me to go into further detail about this part.\r<BR>\n" );
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document.write( "The vertex points are:<BR>\n" );
document.write( "A = (0, 0)<BR>\n" );
document.write( "B = (0, 40)<BR>\n" );
document.write( "C = (12, 28)<BR>\n" );
document.write( "D = (33, 0)<BR>\n" );
document.write( "Each vertex point is found by intersecting the boundary lines. For example, point C is the intersection of the boundary lines 8x+6y = 264 and x+y = 40. \r<BR>\n" );
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document.write( "\"the profit on a trick ski is ​$40 and the profit on a slalom ski is ​$50​\"\r<BR>\n" );
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document.write( "40x = profit from only the trick skis (sold at $40 each)<BR>\n" );
document.write( "50y = profit from only the slalom skis (sold at $50 each)<BR>\n" );
document.write( "P = total profit (both types of skis)<BR>\n" );
document.write( "P = 40x + 50y\r<BR>\n" );
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document.write( "Plug each vertex point into the profit function\r<BR>\n" );
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document.write( "Plug in (x,y) = (0,0)<BR>\n" );
document.write( "P =  40x + 50y<BR>\n" );
document.write( "P =  40(0) + 50(0)<BR>\n" );
document.write( "P = 0<BR>\n" );
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document.write( "Plug in (x,y) = (0,40)<BR>\n" );
document.write( "P =  40x + 50y<BR>\n" );
document.write( "P =  40(0) + 50(40)<BR>\n" );
document.write( "P = 2000<BR>\n" );
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document.write( "Plug in (x,y) = (12,28)<BR>\n" );
document.write( "P =  40x + 50y<BR>\n" );
document.write( "P =  40(12) + 50(28)<BR>\n" );
document.write( "P = 1880<BR>\n" );
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document.write( "Plug in (x,y) = (33,0)<BR>\n" );
document.write( "P =  40x + 50y<BR>\n" );
document.write( "P =  40(33) + 50(0)<BR>\n" );
document.write( "P = 1320<BR>\n" );
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document.write( "Summary:<BR>\n" );
document.write( "Min is P = 0 which occurs at (x,y) = (0,0)<BR>\n" );
document.write( "Max is P = 2000 which occurs at (x,y) = (0,40)\r<BR>\n" );
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document.write( "To get the max daily profit of $2000 per day, you need to make x = 0 trick skis per day and y = 40 slalom skis per day.\r<BR>\n" );
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document.write( "Side note: If both x and y must be greater than zero, then the next highest profit possible is when (x,y) = (12,28). This profit is $1880 per day.<BR>\n" );
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