Profit maximisation  Producers are considered to be rational and profit maximisers. For that they need to minimise their cost of production and maximize the output.  To minimise the input cost, producers tend to use those inputs which cost least. So the least – cost combination of inputs helps the firm to minimise its cost of production based on the principle of equi-marginal returns.

 For example, if a rupee spent on factor A enhances output more than that obtained from a rupee spent on factor B, then a producer would substitute factor A for factor B.  It will continue until equilibrium when marginal returns of the two factors are equal over the unit of money spent.

 The principle of least cost combination has certain limitations : (i)the factors may not be perfectly divisible and effective substitution may not be possible; (ii)there are difficulties in calculating the marginal product of each factor and (iii)the producer has to decide not only the best production of factors, but also the best scale of production. Thus, there are limitations in the use of the principle of least cost combination.

Linear programming  Linear programming is one of the widely used techniques in managerial decision making. It is essentially a problem of either maximizing (say, income) or minimizing (say, cost) a function of several variables subject to certain constraints.  As resources are scarce and have alternative uses we are often encountered with the problem of best choice to ensure that the resources were used in the most advantageous way.

 However, we may have several options and frequently it may not be all that simple to find out that best “option” by working on manual methods.  However, using the linear programming technique, these problems could be solved in a computer in few minutes.

The Linear Programming 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.

Applications of the L.P. techniques  Several applications of the linear programming technique in the case of fisheries are possible. In aquaculture, for example, suppose we need to formulate a feed of a certain protein content using about 30 ingredients in varying ratios.  Further, if the desired feed of specific protein content need to be a least cost one, then, this could be done using linear programming technique

 In fish processing, several ingredients could be used in varying proportions in more than one processing method to manufacture a product at the minimum cost possible.  One may wish to know the optimum fish production plan in carp culture or marine fishing. All these problems could easily be solved using the linear programming technique.