The external "b" area is not convex, thus it is not possible to answer
your question by solving a single LP problem according to your
formulation.

Why don't you compute the intersection of a and b (both internal areas)?

In that way you only need to solve a single LP as you have convex
domains, and you only have to decide if the LP problem is feasible.

What do you use these kind of problems for?

I deal with interval methods where we have very similar problems.

Good luck,

Ali


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