document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205183>Question 1205183</A>: <I><SPAN STYLE=\"word-break: break-all;\"> \"Extremista\" produces two products, A and B, which have profits of $9 and $7, respectively. Each unit of product must be processed on two assembly lines, where the required production times are as follows:\r<BR>\n" );
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document.write( "Product                Hours/Unit<BR>\n" );
document.write( "                               Line 1        Line 2<BR>\n" );
document.write( "A                              12                  4<BR>\n" );
document.write( "B                                4                  8<BR>\n" );
document.write( "Total hours             60               40\r<BR>\n" );
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document.write( "a. Formulate a Linear Programing model and determine the optimal mix of products that will<BR>\n" );
document.write( "maximize profits. (9 marks)<BR>\n" );
document.write( "b. Sketch the graph of the model you have developed. (5 marks)<BR>\n" );
document.write( "c. What would be the effect on the optimal solution if the profit for Product B was moved from<BR>\n" );
document.write( "$7 to $15. (6 marks) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841857 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=841857\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your objective function is 9x + 7y which you want to maximize.\r<BR>\n" );
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document.write( "your constraint inequalities are:<BR>\n" );
document.write( "12x + 4y <= 60<BR>\n" );
document.write( "4x + 8y <= 40\r<BR>\n" );
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document.write( "using the desmos.com calculator, you would:<BR>\n" );
document.write( "graph the opposite of the inequalities.<BR>\n" );
document.write( "the area on the graph not shaded is the region of feasibility.<BR>\n" );
document.write( "at least one of the corner points of this region contain he maximum profit.<BR>\n" );
document.write( "you find this by evaluating the objective function at each corner point.\r<BR>\n" );
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document.write( "this is what the graph looks like.\r<BR>\n" );
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document.write( "maximum profit is at the coordinate point of (4,3).<BR>\n" );
document.write( "the profit is 4 * 9 + 3 * 7 = 57<BR>\n" );
document.write( "all the constraints are satisfied, as they need to be.<BR>\n" );
document.write( "12x + 4y = 12 * 4 + 4 * 3 = 60 <= 60<BR>\n" );
document.write( "4x + 8y = 4 * 4 + 8 * 3 = 40 <= 40\r<BR>\n" );
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document.write( "if the profit for product B was 15 instead of 7, .....<BR>\n" );
document.write( "the constraints would remain the same.<BR>\n" );
document.write( "the profit for each option:<BR>\n" );
document.write( "at (0,5) would become 0 * 9 + 5 * 15 = 75 instead of 0 * 9 + 5 * 7 = 35.<BR>\n" );
document.write( "at (4,3) would become 4 * 9 + 3 * 15 = 81 instead of 4 * 9 + 3 * 7 = 57.<BR>\n" );
document.write( "at (5,0) would become 5 * 9 + 0 * 15 = 45 same as 5 * 9 + 0 * 7 = 45.<BR>\n" );
document.write( "the maximum profit would remain at (4,3).<BR>\n" );
document.write( "that means 4 units of product A plus 3 units of product B. </SPAN>\n" );
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