ax < b representing m linear constraints with right-hand side b. a is an m × n matrix with total coefficients (Hazell and Norton 1986) (Fig. 8).
From the perspective of superimposing the theoretical model image on the
conceptual model image, the terminology in view of mathematical modeling is
described in the following sections that how the theoretical components T
1
–T
6
(Fig. 7) become part of conceptual model system MODAM C
1
–C
6 (Fig. 9).
8.1 Restrictions (T
1 C
1 )
These are constraints and represent the drivers; visualizing their presence in the
landscape scenario, the farmer has to act accordingly and to opt for the feasible
alternatives where these restrictions are making minimal hurdles. These are
expressed as external variables such as environmental resources (land availability,
climatic conditions), socioeconomic resources (labor and capital), policies (subsidies, nature conservation strategies), and national economy (competition for labor
and capital). The quantification of variables delivers the left-hand side of the LP
equation system. In an LP modeling system the ecological restrictions are derived
from the environmental resources, while socioeconomic, political, and national
economy factors become the economic restrictions.
8.2 Goal Function (T
2 C
2
)
Goal function simulates the decision making of farmers in terms of maximizing
their income. Therefore, the model chooses several activities out of manifold
activities that best utilize given resources and which are restricted by external
factors such as environmental or political factors. This procedure leads to maximization of income level.
Reality
Reality
Model
Theory
or
Subject
Model
Theory
or
Subject
Fig. 8 Model is the part of
its reality as its subject or
theory (Gonzalez-Perez and
Henderson-Sellers 2007)
618
S. Nautiyal et al.
From the perspective of superimposing the theoretical model image on the
conceptual model image, the terminology in view of mathematical modeling is
described in the following sections that how the theoretical components T
1
–T
6
(Fig. 7) become part of conceptual model system MODAM C
1
–C
6 (Fig. 9).
8.1 Restrictions (T
1 C
1 )
These are constraints and represent the drivers; visualizing their presence in the
landscape scenario, the farmer has to act accordingly and to opt for the feasible
alternatives where these restrictions are making minimal hurdles. These are
expressed as external variables such as environmental resources (land availability,
climatic conditions), socioeconomic resources (labor and capital), policies (subsidies, nature conservation strategies), and national economy (competition for labor
and capital). The quantification of variables delivers the left-hand side of the LP
equation system. In an LP modeling system the ecological restrictions are derived
from the environmental resources, while socioeconomic, political, and national
economy factors become the economic restrictions.
8.2 Goal Function (T
2 C
2
)
Goal function simulates the decision making of farmers in terms of maximizing
their income. Therefore, the model chooses several activities out of manifold
activities that best utilize given resources and which are restricted by external
factors such as environmental or political factors. This procedure leads to maximization of income level.
Reality
Reality
Model
Theory
or
Subject
Model
Theory
or
Subject
Fig. 8 Model is the part of
its reality as its subject or
theory (Gonzalez-Perez and
Henderson-Sellers 2007)
618
S. Nautiyal et al.