Fisheries Economics

5.1.3. The l.p. problem

It is very important that we write down the linear programming problem clearly and correctly. Otherwise, the results obtained may not be meaningful. We need to specify the decision variables, the objective function and the constraints for the linear programming problem irrespective of whether it involves maximization or minimisation. Let us take carp farming as an example. The important inputs used in carp culture are : pond area (optional), manure, urea, super phosphate, fingerlings stocked, groundnut oilcake, rice bran and labour. These variables are therefore the decision variables. Then, we should write down the objective function which spells the contribution of each of these inputs for a particular levels of output.

In the case of fish culture, the objective function may mean total yield of carps farmed and harvested or total income obtained. In case the yield is to be maximized, then all the physical inputs should be included as decision variables. On the other hand, if income maximization is attempted then information on prices, consumer preferences and demand, supply of substitution products and their prices etc. would need to be incorporated. The constraints with reference to the various decision variables, pond area, water availability, capital etc. should be specified. With these, a linear problem could be formulated for obtaining an optimal solution. It should be noted that clear and precise formulation of the problem is important as otherwise meaningful inferences could not be drawn from the results so obtained.

Solution

Calculus and matrix algebra could be used to solve the problem manually. Graphical method could also be used. However, when the variables and data set are large, then, it may be infeasible to work out manually. Therefore, the problem should be run in a computer using an appropriate software.