Abstract - Linear Programming technique was applied to farm
data of a representative sample of farmers involved in arable
crop farming in combination with mono gastric farm animals
and fish farming. Thirty farmers were selected from three
villages within three circles in a chosen block by means of
multi-stage stratified random sampling technique. Primary
data were collected using well structured questionnaire on
resource use and availability, input and output prices, types of
enterprise combination etc. of the representative farms using
the cost-route approach in Ohafia zone of Abia State, during
the 2010 farming season. Data were analyzed using linear
programming. The study was to solve a maximization problem
of gross margin among combination of existing enterprises by
this category of farmers. The programme recommended yam
(0.29ha), cassava (0.02ha) and cassava/maize/cocoyam
(0.13ha), broiler I – August – December (70.00 birds), fish I
(220.00 fish) and layers (205.00 birds) enterprises for an
average farmer in Ohafia to optimize gross margin given the
available resources. Optimum gross margin for Ohafia was
72.90% greater than obtained in the existing plan. Yam/melon
had the least shadow price of N428.34 in the study area. It
was only feed that constrained the attainment of the objective
function. When land was increased by 50% of what was
available, gross margin obtained was insensitive. Based on
the findings of the study therefore, given more lands to the
farmers would not make for increased gross margin. It is rather
policies that will improve extension services for the farmers in
their livestock management and livestock input subsidy that
could help farmers to maximize gross returns less the variable
costs of production. Adopting the prototype enterprise
combination has tremendous implication on improving the
family income of an average sampled farmer in the study area.
Keywords : linear programming, gross margin,
enterprises, existing plan, optimum plan.