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Formulation

Min $z$
subject to constraints

  • $z \ge x_1+x_2+x_3+x_4-4$
  • $z \ge x_5+x_6+x_7+x_8-60$
  • $z \ge x_9+x_{10}+x_{11}+x_{12}$
  • $x_1+x_5+x_9 \ge 450$
  • $x_2+x_6+x_{10} \ge 200$
  • $x_3+x_7+x_{11} \ge 300$
  • $x_4+x_8+x_{12} \ge 300$
  • $131x_1+218x_{2}+266x_{3}+120x_{4}+250x_{5}+115x_{6}+263x_{7}+278x_{8}+178x_{9}+132x_{10}+122x_{11}+180x_{12} \ge 17000000$
  • $x_i\ge0$ for $i=1,2,\dots,12$

Can anyone tell me how to calculate this objective function in the simplex method? If there is no $x$ in the objective function, then how do I build up the tabular form?

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1 Answer 1

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The $z$ is just another variable. If it helps, rewrite $z$ as $x_{13}$, and then the objective coefficient vector is $(0,0,0,0,0,0,0,0,0,0,0,0,1)$.

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