document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191259>Question 1191259</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Direction: Solve the given problem involving system of linear inequalities by graphing. Andrea does a small business at home. It takes her 2 hours to make a gallon of ice cream (x) and 1 hour for a gallon of concentrated mango juice (y). She can work no more than 10 hours per week. The cost to make a gallon of ice crcam is Php200.00 and the cost to make a concentrated mango juice is Php100.00. She can afford to spend no more than Php2,000.00 per week. Give 3 possible amounts of ice cream and mango juice that Andrea can spend. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #823109 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=823109\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> with the desmos.com calculator, you woud do the following:\r<BR>\n" );
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document.write( "graph the opposite of the inequalities.<BR>\n" );
document.write( "the area on the graph that is not shaded is your region of feasibility.<BR>\n" );
document.write( "any coordinate points within the region of feasibility are valid.<BR>\n" );
document.write( "since the inequalities are <=, then any values on the lines formed are also valid.\r<BR>\n" );
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document.write( "here's what the graph looks like.\r<BR>\n" );
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document.write( "3 coordinate points in the region of feasibility  have been chosen,.\r<BR>\n" );
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document.write( "they are (1,6), (2,4), 3,2).\r<BR>\n" );
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document.write( "the coordinate points are in (x,y) format.<BR>\n" );
document.write( "for example, the coordinate point of (1,6) means the value of x is 1 and the value of y is 6.\r<BR>\n" );
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document.write( "all of the inequalities have to be satisfied at each of the coordinate points.<BR>\n" );
document.write( "with (1,6), ....<BR>\n" );
document.write( "2x + y <= 10 becomes 2 + 6 <= 10 which becomes 8 <= 10 which is true.<BR>\n" );
document.write( "200x + 100y <= 2000 becomes 400 + 100 <= 2000 which becomes 500 <= 2000 which is true.\r<BR>\n" );
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document.write( "the controlling factor on the graph is the number of hours.<BR>\n" );
document.write( "that's why the region of feasibility is on or below the constraint of 2x + y <= 10<BR>\n" );
document.write( "it is possible to satisfy 200x + 100y <= 2000 and not satisfy 2x + y <= 10.<BR>\n" );
document.write( "an example is the point (3,8).<BR>\n" );
document.write( "200x + 100y = 600 + 800 = 1400 <= 2000.<BR>\n" );
document.write( "2x + y = 6 + 8 = 14 which is not <= 10<BR>\n" );
document.write( "the coordinate point of (3,8) is not feasible because it does not satisfy all of the constraints, only some.\r<BR>\n" );
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