With this general background, let us investigate the properties of
 LP and QP problems.


 2.2 Linear Programming


 A linear programming problem is commonly:stated in the following
 manner.
 Maximize
 (Ll) c'x

 subject to the restriction that


 Ax < b
 (L2)
 (L2) x >0


where c and b are known vectors, A is a known matrix, and x is a vector
of variable activities which are controlled by a decisionmaker. The
constraints Ax < b and x > 0 mark off a set of points in a product space
which represent the set of choices available to the decisionmaker due to
technological, economic, and institutional constraints. The objective
of the problem is to choose one point R which is in this set and which
makes the product c'x as large as possible. The term c'x is the objective
function which may, for example, represent net profit associated with the
set of activities chosen.
 The necessary conditions for the saddle value solution of this LP
problem can be stated as follows:


(L3) c A 0 and (c A ) x = 0; (NL1)

(L4) b Ax > 0 and (b- Ax) = 0; (NL2)
and

(L5) x> 0 and 5 > 0; (NL3).

 Condition (L4) states that the primal constraints must be satisfied
and that for each non-binding constraint, the shadow price or dual
activity associated with it must be zero. This concept is central to our
discussion and should be considered carefully. In the context of LP,