document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1062651>Question 1062651</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A hospital dietician wishes to prepare a corn and squash vegetable dish that will provide at least 3 grams of protein and cost no more than 36¢ per serving.  An ounce of creamed corn provides 1÷2 gram of protein and costs 4¢.  An ounce of squash supplies 1÷4 gram of protein and costs 3¢.  There must be at least 2 ounces of corn and at least as much squash as corn.  It is important to keep the total number at ounces in a serving as small as possible.  Find the combination of corn and squash that will minimize the amount of ingredients used per serving? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #678499 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=678499\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> as i understand your problem:\r<BR>\n" );
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document.write( "corn and squash dinner to provide at least 3 grams of protein and cost no more than 36 cents per serving.\r<BR>\n" );
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document.write( "1 ounce of creamed corn provgides 1/2 gram of protein and costs 4 cents.<BR>\n" );
document.write( "1 ounce of squash supplies 1/4 gram of protein and costs 3 cents.\r<BR>\n" );
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document.write( "you need at least 2 ounces of corn.<BR>\n" );
document.write( "you also need at least 2 ounces of squash as well.\r<BR>\n" );
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document.write( "you need to keep the total amound of ounces of corn and squash to a minimum.\r<BR>\n" );
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document.write( "the total cost must be less than 36 cents per serving.\r<BR>\n" );
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document.write( "let x equal the number of ounces of corn.<BR>\n" );
document.write( "let y equal the number of ounces of squash.\r<BR>\n" );
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document.write( "your objective function would be x + y.<BR>\n" );
document.write( "that's what you want to minimize.\r<BR>\n" );
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document.write( "your cost will be 4x + 3y and it has to be less than or equal to 36 cents.\r<BR>\n" );
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document.write( "your constraint function for cost will be 4x + 3y <= 36\r<BR>\n" );
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document.write( "you will need at least 2 ounces of corn and 2 ounces of squash.\r<BR>\n" );
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document.write( "your constraint functions for weight will be:\r<BR>\n" );
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document.write( "x >= 2<BR>\n" );
document.write( "y >= 2\r<BR>\n" );
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document.write( "the total amount of protein must be at least 3 grams.\r<BR>\n" );
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document.write( "your constraint function for protein will be 1/2 * x + 1/4 * y >= 3\r<BR>\n" );
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document.write( "summarizing.\r<BR>\n" );
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document.write( "objective function is to minimize x + y\r<BR>\n" );
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document.write( "constraint functions are:\r<BR>\n" );
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document.write( "x >= 2<BR>\n" );
document.write( "y >= 2\r<BR>\n" );
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document.write( "4x + 3y <= 36\r<BR>\n" );
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document.write( "1/2 * x + 1/4 * y >= 3\r<BR>\n" );
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document.write( "you would graph these functions and find the area of the curve that satisfies all the constraints.\r<BR>\n" );
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document.write( "my graph would look like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/010801.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "i would graph the equalities and then look for the region of feasibility that satisfies the inequalities.\r<BR>\n" );
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document.write( "the equations i graphed are:\r<BR>\n" );
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document.write( "x = 2<BR>\n" );
document.write( "y = 2<BR>\n" );
document.write( "4x + 3y =36<BR>\n" );
document.write( "1/2 * x + 1/4 * y = 36\r<BR>\n" );
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document.write( "the region of feasibility is the region on the graph that satisfies the inequalities.\r<BR>\n" );
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document.write( "that area would be where:\r<BR>\n" );
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document.write( "x >= 2<BR>\n" );
document.write( "y >= 2<BR>\n" );
document.write( "4x + 3y <= 36<BR>\n" );
document.write( "1/2 * x + 1/4 * y >= 3\r<BR>\n" );
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document.write( "the arrows from the lines indicate where the region of feasibility lies.<BR>\n" );
document.write( "anywhere in that region between those lines is the feasible region.<BR>\n" );
document.write( "all the constraints are satisfied within that region.\r<BR>\n" );
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document.write( "i would then look for the corners of the region of feasibility and evaluate the objective function at those corners.<BR>\n" );
document.write( "the maximum or minimum value for the feasible region would be found at those corners.\r<BR>\n" );
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document.write( "the corners of the region of feasibility are:\r<BR>\n" );
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document.write( "(2,9+1/3)<BR>\n" );
document.write( "(2,8)<BR>\n" );
document.write( "(5,2)<BR>\n" );
document.write( "(7.5,2)]\r<BR>\n" );
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document.write( "the objective function is x + y which leads to:\r<BR>\n" );
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document.write( "11+1/3<BR>\n" );
document.write( "10<BR>\n" );
document.write( "10<BR>\n" );
document.write( "9.5\r<BR>\n" );
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document.write( "at each of those respective corner points.\r<BR>\n" );
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document.write( "the minimum number of ounces is at (7.5,2) where the total number of ounces are 7.5 + 2 = 9.5.\r<BR>\n" );
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document.write( "the constraints are satisfied at that point because:\r<BR>\n" );
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document.write( "x = 7.5 which is >= 2<BR>\n" );
document.write( "y = 2 which is >= 2<BR>\n" );
document.write( "4x + 3y = (4 * 7.5) + (3 * 2) = 30 + 6 = 36 which is <= 36<BR>\n" );
document.write( "1/2 * x + 1/4 * y = (1/2 * 7.5) + (1/4 * 2) = 3.25 + .5 = 3.75 which is >= 3\r<BR>\n" );
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document.write( "you were able to minimize the number of ounces while still satisfying the constraints.\r<BR>\n" );
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document.write( "your solution should be 7.5 ounces of corn and 2 ounces of squash will be the minimum amount of total ingredients that you need to satisfy the requirements.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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