Suppose you have the following Linear Programming problem P(adsbygoogle = window.adsbygoogle || []).push({});

Max

[tex]z = ax + by[/tex]

s.t.

[tex]cx + dy = E[/tex]

[tex]fx + gy = H[/tex]

For [tex]x,y, \geq 0[/tex]

Suppose I also tell you that the region formed by the two constraints are unbounded and hence the corner points of the feasible region will tell you only the min. (so something like either [tex]x \geq M[/tex] or [tex]y \geq M[/tex] for some M) Can you comment that the linear programming problem P is also unbounded?

SO my take is that if cx + dy = E and fx + gy = H are parallel and if somehow the constraints [tex]x,y, \geq 0[/tex] could disappear, I would get an unbounded feasible region and you could theoretically change z to get an optimal.

But what if z is fixed? Or [tex]x,y, \geq 0[/tex] has to stay?

Any takers?

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# Is this theory correct? Unbounded set implies unbounded optimium (2D only)

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