Consider the mathematical program
Consider the mathematical program
$$ \begin{array}{ll} \max & 3 x_{1}+x_{2}+3 x_{3} \\ \text { s.t. } & 2 x_{1}+x_{2}+x_{3}+x_{4}=2 \\ & x_{1}+2 x_{2}+3 x_{3}+2 x_{5}=5 \\ & 2 x_{1}+2 x_{2}+x_{3}+3 x_{6}=6 \\ & x_{1}, x_{2}, x_{3}, x_{4}, x_{5}, x_{6} \geq 0 \end{array} $$
Three feasible solutions ((a) through (c)) are listed below.
(a) \(x^{(0)}=(0.2,0.1,0.3,1.2,1.85,1.7)\)
(b) \(\mathbf{x}^{(0)}=(0.9,0,0,0.2,2.05,1.4)\)
(c) \(\mathbf{x}^{(0)}=(0.3,0.1,0.4,0.9,1.65,1.6)\)
Please choose one appropriate interior point from the list, and use the Karmarkar's Method at the interior point and determine the optimal solution.
Homework Answers
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