document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187163>Question 1187163</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sarah has $8 and wants to buy a combination of cupcakes and fudge to feed at least four siblings. Each cupcake costs $2, and each piece of fudge costs $1.\r<BR>\n" );
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document.write( "This system of inequalities models the scenario:\r<BR>\n" );
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document.write( "2x + y ≤ 8<BR>\n" );
document.write( "x + y ≥ 4\r<BR>\n" );
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document.write( "Part A: Describe the graph of the system of inequalities, including shading and the types of lines graphed. Provide a description of the solution set. (4 points)\r<BR>\n" );
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document.write( "Part B: Is the point (8, 10) included in the solution area for the system? Justify your answer mathematically. (3 points)\r<BR>\n" );
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document.write( "Part C: Choose a point in the solution set and interpret what it means in terms of the real-world context. (3 points) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #820793 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=820793\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x is the number of cupcakes.<BR>\n" );
document.write( "y is the number of fudge pieces.\r<BR>\n" );
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document.write( "2x + y <= 8 is the inequality for the cost.\r<BR>\n" );
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document.write( "x + y >= 4 is the inequality for the number of cupcakes or pieces of fudge that she wants to buy.\r<BR>\n" );
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document.write( "using the desmos.com calculator, you would graph the OPPOSITE of the inequalities.<BR>\n" );
document.write( "the area on the graph that is NOT shaded is the feasible region.\r<BR>\n" );
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document.write( "the graph looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/010901.jpg\" >\r<BR>\n" );
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document.write( "the solution set is all integral coordinate points that are either on the lines x + y = 4 or 2x + y = 8 or x = 0 or anywhere in the unshaded area of the graph.\r<BR>\n" );
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document.write( "specifically, the coordinate points that are acceptable are:<BR>\n" );
document.write( "(0,8)<BR>\n" );
document.write( "(0,7)<BR>\n" );
document.write( "(0,6)<BR>\n" );
document.write( "(0,5)<BR>\n" );
document.write( "(0,4)<BR>\n" );
document.write( "(1,6)<BR>\n" );
document.write( "(1,5)<BR>\n" );
document.write( "(1,4)<BR>\n" );
document.write( "(1,3)<BR>\n" );
document.write( "(2,4)<BR>\n" );
document.write( "(2,3)<BR>\n" );
document.write( "(2,2)<BR>\n" );
document.write( "(3,2)<BR>\n" );
document.write( "(3,1)<BR>\n" );
document.write( "(4,0)\r<BR>\n" );
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document.write( "the point (8,10) is not included in the solution set because it is not in the unshaded area on the graph.\r<BR>\n" );
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document.write( "it does not meet the constraint requirements.<BR>\n" );
document.write( "(8,10) means x = 8 and y = 10<BR>\n" );
document.write( "x + y = 18 is satisfied because the constraint is x + y >= 4.<BR>\n" );
document.write( "the constraint 2x + y <= 8 is not satisfied because 2x + y = 26 which is NOT smaller than or equal to 8.<BR>\n" );
document.write( "ALL the constraints have to be satisfied at each coordinate point.<BR>\n" );
document.write( "otherwise that coordinate point is not acceptable.\r<BR>\n" );
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document.write( "take any of the points that are feasible and test them out.<BR>\n" );
document.write( "you will find that each of them meets ALl of the constraints.<BR>\n" );
document.write( "for example:<BR>\n" );
document.write( "(4,0) meets the constraints because x + y >= 4 and 2x + y <= 8<BR>\n" );
document.write( "this cross point would buy 4 cupcakes and no pieces of fudge.\r<BR>\n" );
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document.write( "at the other extreme, (0,8) is feasible because x + y >= 4 and 2x + y <= 8.<BR>\n" );
document.write( "this cross point would buy 8 pieces of fudge and no cupcakes.\r<BR>\n" );
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document.write( "the real world context has been explained for both of these points.\r<BR>\n" );
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document.write( "the real world context for (8,10) would be explained as:<BR>\n" );
document.write( "x + y = 8 cupcakes and 10 pieces of fudge, the combination of which are greater than or equal to 4.<BR>\n" );
document.write( "2x + y =  16 + 10 = 26 dollars which is NOT less than or equal to 8.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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