programming in general and quadratic programming and linear complementary
programming in particular.
 The fundamental concern which motivates alternatives to linear pro-
gramming is the concern of the economist to develop models which repre-
sent a market situation rather than merely the perspective of"an indiv-
idual decisionmaker. In particular, there is no way in LP to include
both market prices and quantities as continuous endogenous variables,
The reality of spatially distinct markets separated by a transportation
cost with each market having its own set of continuous demand and supply
functions can not be represented.
 Quadratic programming provides a method for handling the above pro-
blems in a convenient manner. The mathematics of the approach is non-
trivial and is fully covered in [5]. Conceptually and practically,
however, the approach is fairly simple.
 The general QP problem has the following form:

 Maximize


(Ql) c'x l/2x'Qx

subject to

 Ax < b
(Q2)
C( 2)x > 0


As in the LP problem, c and b are known (fixed) vectors, and A is a
known matrix. The vector x is a set of unknown variables, and in this
case, Q is a known symmetric, positive semi-definite matrix.
 In the case of market-oriented QP models, the objective function is
created by generating the sum of consumers' and producers' surplus, and
subtracting any fixed costs associated with transportation or production.
The c'x portion of the objective function consists of the linear costs
for production and transportation and the intercepts of the demand and
supply functions. The quadratic terms of the objective function arise
from the integration of linear demand and supply functions done to
measure consumer's plus producer's surplus.
 The Ax < b constraint set describes the material availability and
requirement balance relationships, capacity constraints, etc. in the
model.