document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197130>Question 1197130</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You want at least 16g of protein and no more than 50g of carbs at a meal. 1oz of X has 9g of protein and 12g of carbs. 1oz of Y has 4g of protein and 10g of carbs. You want to eat at least 2oz total food at this meal.<BR>\n" );
document.write( "-Identify (name) the 3 constraints and write them as a set of inequalities.<BR>\n" );
document.write( "-What combination allows you to eat the minimum ozs of food while also eating exactly 16g of protein? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #830290 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=830290\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = number of ounces of product X.<BR>\n" );
document.write( "y = number of ounces of product Y.\r<BR>\n" );
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document.write( "your constraint inequalities are:<BR>\n" );
document.write( "9x + 4y >= 16 (ounces of protein constraint)<BR>\n" );
document.write( "12x + 10y <= 50 (ounces of carb constraint)<BR>\n" );
document.write( "x + y >= 2 (total ounces constraint)<BR>\n" );
document.write( "x >= 0<BR>\n" );
document.write( "y >= 0<BR>\n" );
document.write( "9x + 4y = 16\r<BR>\n" );
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document.write( "the first 3 are the inequalities you are looking for.<BR>\n" );
document.write( "the next 2 are for graphing purposes to make sure the ounces of either product are greater than or equal to 0.<BR>\n" );
document.write( "the last one is to identify where exactly 16 grams of protein are situated on the graph.\r<BR>\n" );
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document.write( "your objective function is x + y because you want to find the minimum number of ounces of food that give you exactly 16 ounces of protein.\r<BR>\n" );
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document.write( "using the desmos.com calculator, you would graph the opposite of the inequalities and you would evaluate the objective function at the corner points of the feasible region.\r<BR>\n" );
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document.write( "the feasible region is the area on the graph that is not shaded.\r<BR>\n" );
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document.write( "you can see from the graph that your solution will lie on the line of the equation of 9x + 4y = 16<BR>\n" );
document.write( "there are two possibilities.<BR>\n" );
document.write( "(x,y) = (0,4) and (1.6,.4)<BR>\n" );
document.write( "the objective function is x + y.<BR>\n" );
document.write( "that's what you want to minimize.<BR>\n" );
document.write( "at (0,4), x + y = 4<BR>\n" );
document.write( "at (1.6,.4), x + y = 2\r<BR>\n" );
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document.write( "the minimum ounces of food that contain exactly 16 grams of protein are 1.6 ounces of product X and .4 ounces of product Y.\r<BR>\n" );
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document.write( "here's your graph.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/101201.jpg\" >\r<BR>\n" );
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document.write( "let me know if you have any questions regarding this.<BR>\n" );
document.write( "theo\r<BR>\n" );
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