document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204971>Question 1204971</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Andre is organizing a charity event where he plans to sell two types of items: T-shirts and hats. The selling price for a T-shirt is $15, and the selling price for a hat is $10. Andre wants to sell at least 50 items in total and make a minimum of $600 in sales. If he knows that he can sell at most 40 T-shirts, and he wants to sell at least twice as many T-shirts as hats, how many of each item should he sell to meet his goals? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841552 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52847)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=841552\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Andre is organizing a charity event where he plans to sell two types of items: T-shirts and hats. <BR>\n" );
document.write( "The selling price for a T-shirt is $15, and the selling price for a hat is $10. <BR>\n" );
document.write( "Andre wants to sell at least 50 items in total and make a minimum of $600 in sales. <BR>\n" );
document.write( "If he knows that he can sell at most 40 T-shirts, and he wants to sell at least twice as many <BR>\n" );
document.write( "T-shirts as hats, how many of each item should he sell to meet his goals?<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "This problem is on solving a system of inequalities in integer non-negative numbers.\r\n" );
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document.write( "Let x be the number of T-shirt;\r\n" );
document.write( "    y be the number of hats.\r\n" );
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document.write( "The inequalities are\r\n" );
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document.write( "      x +   y >= 50    (1)     (Andre wants to sell at least 50 items in total)\r\n" );
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document.write( "    15x + 10y >= 600   (2)     (Andre wants to make a minimum of $600 in sales)\r\n" );
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document.write( "      x       <=  40   (3)     (he can sell at most 40 T-shirts_\r\n" );
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document.write( "      x       >=  2y   (4)     (he wants to sell at least twice as many T-shirts as hats)\r\n" );
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document.write( "      x >= 0,  y >= 0  (5)     (standard non-negativity inequalities)\r\n" );
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document.write( "Next you take a graph paper and draw the corresponding lines and mark corresponding areas.\r\n" );
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document.write( "Your solution are integer points of the graph paper in the intersection of all areas (if such points do exist).\r\n" );
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document.write( "It is \"WHAT to do\" and \"HOW to do\" to solve the problem on your own.\r<BR>\n" );
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document.write( "The problem may have more than one solution, but it is not a catastrophic event - it is very normal, if it is so.\r<BR>\n" );
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document.write( "It is a standard procedure to solve a school problem on inequalities in integer numbers in 2D plane <BR>\n" );
document.write( "(= for two variables) graphically.\r<BR>\n" );
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document.write( "To facilitate your job, you can use free of charge plotting tool at web-site\r<BR>\n" );
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document.write( "www.desmos.com/calculator\r<BR>\n" );
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document.write( "In this case, you should print each and every inequality (1) - (5) in their specialized window.\r<BR>\n" );
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document.write( "The intersection of all relevant regions is the solution set, and you need integer points of the grid in the solution set.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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