document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1059142>Question 1059142</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this word problem:<BR>\n" );
document.write( "You can spend at most $21 on fruit.  Blueberries cost $4 per pound and strawberries cost $3 per pound.  You need at least 3 pounds to make muffins.<BR>\n" );
document.write( "a. Define the variables.<BR>\n" );
document.write( "b. Write a system of linear inequalities that represents this situation.<BR>\n" );
document.write( "c. Graph the system of linear inequalities.<BR>\n" );
document.write( "d. Is it possible to buy 4 pounds of blueberries and 1 pound of straberries in this situation? Justify your answer. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #674246 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=674246\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x equal the pounds of blueberries.<BR>\n" );
document.write( "let y = the pounds of strawberries.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "blueberries cost 4 dollars a pound.<BR>\n" );
document.write( "strawberries cost 3 dollars a pound.<BR>\n" );
document.write( "total cost has to be less than 21 dollars.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "equation for that is:<BR>\n" );
document.write( "4x + 3y <= 21\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you need at least 3 pounds of fruit to make muffins.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "equation for that is:<BR>\n" );
document.write( "x + y >= 3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "is it possible to buy 4 pounds of blueberries and 1 pound of strawberries in this scenario?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "4 pounds of blueberries costs 4 * 4 = 16 dollars.<BR>\n" );
document.write( "1 pound of strawberries costs 3 * 1 = 3 dollars.<BR>\n" );
document.write( "total cost is 19 dollars which is less than the maximum amount of money than can be spent.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "5 pounds of fruit is greater than the minimum amount of fruit required.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "answer is yes.<BR>\n" );
document.write( "all the requirements are met.<BR>\n" );
document.write( "pounds of fruit need to be greater than 3.<BR>\n" );
document.write( "dollars of cost need to be less than 21.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "following graph shows this relationship.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/112902.jpg\" alt=\"$$$\" </>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in this graph, the area that is NOT shaded represents the region of feasibility.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since 4x + 3y <= 21 represents the area of the graph that satisfies the requirement, then 4x + 3y >= 21 represents the area of the graph that doesn't satisfy the requirement.<BR>\n" );
document.write( "that is the area in the graph that is shaded.<BR>\n" );
document.write( "from 4x + 3y >= 21, solve for y to get y >= (21 - 4x) / 3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since x + y >= 3 represents the area of the graph that satisfies the requirement, then x + y <= 3 represents the area of the graph that doesn't satisfy the requirement.<BR>\n" );
document.write( "that is the area in the graph that is shaded.<BR>\n" );
document.write( "from x + y <= 3, solve for y to get y <= 3 - x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "two implied requirements are that x and y both have to be greater than or equal to 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "therefore, x and y <= 0 do not satisfy that requirement and are therefore shaded as well.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the region of feasibility on the graph is represented by the area of the graph that is NOT shaded.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "why do i do it this way?<BR>\n" );
document.write( "because it's a lot easier to see the region of feasibility when it is not shaded than when it is shaded when i am using software to generate the graph.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if i was generating the graph manually, then i would have just shaded the region of feasibility instead.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in that case, the part that you see not shaded would have been the only part of the graph that was shaded.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );