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I understood that when plotting the feasible area there had to be an intersection with more than two lines.

In the case of:

$$\text{Max } z=2x_1+x_2$$ S.T $$ \begin{cases} 4x_1+3x_2\leq 12\\ 4x_1+x_2 \leq 8\\ 4x_1-x_2 \leq 8\\ x_1,x_2\geq 0 \end{cases} $$

The plot is which mean that there is almost intersection of the there functions, is it still degeneracy?

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Edit: yes this LP admits degenerate solutions, e.g., $(x_1, x_2)=(2,0)$, since the constraints $4x_1+x_2 \leq 8, 4 x_1-x_2 \leq 8, x_2 \geq 0$ are all active at this point, and $3$ active constraints in a 2d space implies degeneracy.

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  • $\begingroup$ But using simplex I get that a basic variable has a value of zero, so it is degenerate right? $\endgroup$ – newhere Apr 17 '19 at 19:27
  • $\begingroup$ Ah right, I missed the non-negativity constraints. Yes, $4x_1+x_2 \leq 8, 4 x_1-x_2 \leq 8, x_2 \geq 0$ are all active at $(x_1, x_2)=(2,0)$, so yes that point is degenerate. $\endgroup$ – Ryan Cory-Wright Apr 17 '19 at 20:44
  • $\begingroup$ But still there is no intersection of 3 or more lines $\endgroup$ – newhere Apr 18 '19 at 8:20
  • $\begingroup$ In your plot, don't $x=0, 4x+y=8, 4x-y=8$ intersect at the same point? $\endgroup$ – Ryan Cory-Wright Apr 18 '19 at 14:12

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