Consider the primal linear program (P) max{cTx•Ax=b,x≥0} with activities x and a resource endowment b. The optimal solutions of the dual program (D)min{bTu•ATu≥c} have a well known economic interpretation as shadow prices of resources. It is possible to pose the dual problem in space of activities, by rewriting (D) as (D)min{ℝ6xTy•y∈R(AT),y≥c} where ℝ6x is any solution of Ax=b. The primal and dual Simplex methods can then be unified using certain canonical bases of the subspaces N(A) and R(AT). In this note the optimal sets of (P) and (D) are given concise symmetric representations using canonical bases, and the optimal y* in (D) are interpreted in terms of support prices of the activities in (P), related to changes in activity levels. These results are applied to activation prices of unused activities and de-activation prices of those in use.
