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3 Answers 3

These notes by Ted Ralphs, Lehigh University, give you an answer to question 2, computing the dimension.

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Question 1 can be answered by forming an artificial problem and applying simplex method (look for two-phase simplex method in google). Question 2: If what you mean by dimension of the solution set is the number of extreme points, then we know from linear programming theory that the number of extreme points will be ${n+m}\choose{m}$, where $n$ is the number of variables and $m$ the number of inequalties. Remember that all interior points in the polyhedron may be represented as convex combinations of the extreme points, so that knowledge of the extreme points is sufficient to characterize all the solution set.

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