document.write( "Question 1142000: Solve the linear programming problem by the method of corners.
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Algebra.Com's Answer #762668 by ikleyn(52790) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "You need to maximize the objective function P(x,y) = x + 6y under given restrictions.\r\n" );
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document.write( "The feasible domain is shown below.\r\n" );
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document.write( "It is  a quadrilateral in the first quadrant  (x >= 0,  y >= 0)  restricted \r\n" );
document.write( "by the red line  x + y = 4  and the green line  2x + y = 7.\r\n" );
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document.write( "Plots  x + y = 4  (red) and  2x + y = 7 (green)\r\n" );
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document.write( "The vertices of this quadrilateral are\r\n" );
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document.write( "        (X0,Y0) = (0,0)     (the origin of the coordinate system);\r\n" );
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document.write( "        (X1,Y1) = (0,4)     (red line Y-intercept);\r\n" );
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document.write( "        (X2,Y2) = (3,1)     (intersection point of the straight lines y = 4-x and  y = 7-2x );\r\n" );
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document.write( "        (X3,Y3) = (3.5,0)   (green line X-intercept)\r\n" );
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document.write( "Calculate the objective function at these points\r\n" );
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document.write( "        P(X0,Y0) = 0 + 6*0   = 0;\r\n" );
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document.write( "        P(X1,Y1) = 0 + 6*4   = 24;\r\n" );
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document.write( "        P(X2,Y2) = 3 + 6*1   =  9;\r\n" );
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document.write( "        P(X3,Y3) = 3.5 + 6*0 =  3.5.\r\n" );
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document.write( "Select one of these points where the objective function is maximal. In our case this point is (X1,Y1) = (0,4).\r\n" );
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document.write( "This point gives your optimal solution x = 0,  y = 4.\r\n" );
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document.write( "The maximum objective function value is 24.\r\n" );
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\n" ); document.write( "\n" ); document.write( "To see many other similar solved problems, look into the lesson\r
\n" ); document.write( "\n" ); document.write( " - Solving minimax problems by the Linear Programming method \r
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\n" ); document.write( "\n" ); document.write( "See also many other similar solved problems in the archive to this forum\r
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\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1137172.html\r
\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/Graphs/Graphs.faq.question.1136382.html\r
\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/Coordinate-system/Coordinate-system.faq.question.1134444.html\r
\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/Graphs/Graphs.faq.question.1131906.html\r
\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/coordinate/word/Linear_Equations_And_Systems_Word_Problems.faq.question.1131043.html\r
\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1129285.html\r
\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1128383.html\r
\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/playground/test.faq.question.1112482.html\r
\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.1123217.html\r
\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1102103.html\r
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\n" ); document.write( "\n" ); document.write( "From these sources, learn the technique and the methodology on how to solve minimax problems using the Linear Programming method - once and for all.\r
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