4. Theory of Linear Programming

Mathematical programming in statistical estimation theory

“…Their paper extends the notion of equivalence between linear programming and saddle value problems [see Goldman and Tucker,14] …”

“…f evaluated at the grid point x*. Because of where .f* i J the convexity of ^f(x) the polyhedral space defined by (14) contains the convex space ^f(x) < ^b entirely. As the grid width of the x* tends to zero the intersection of the polyhedral spaces (14) for i = 1, 2, ..., m tends to that described by (9).…”

The optimal capacity expansion policy for a firm

“…From 125b and 126 we deduce that for any good, i, i e that is produced at a positive level, we must have ; t=0, 1, ..., ^This is lemma 4 on page 59, Goldman and Tucker (1956) where indicates the technically determined utilization rate (the amount of service-flow consumed) of the resource by the i^^ process at the unit level of intensity, i.e., for producing one unit of the i*"^ good, 1=1, 2; j=l, 2.…”

“…determined, as it would be in Q. However, Goldman and Tucker (1956) have shown that if both LP and D are feasible (as they are) then for any j, j e I j the following alternatives will hold:^ n 1. either 2 a..q. <b, for some optimal q and y.…”

“…With appropriate changes in notation, this is Corollary 2B on page 62, Goldman and Tucker (1956). gives the firm's "expansion path" over time.…”