Crop rotation systems in the Swartland

In the Swartland region farmers do not plant wheat exclusively. There are a lot of reasons for this. The main reason is that farmers who plant only one crop will end up with a situation where they will have to buy so much fertiliser that they would not be able to make any money. Every crop influences the crops on the same land later on. It is up to the farmer to decide what the influence will be. That means it is up to the farmer to decide what crop to plant on what land. The farmer ends up rotating a certain number of crops on his land. This rotation of crops is called a rotary crop system. In this situation arises the problem of what sequence of crops should be planted to ensure an optimal income to the farmer without exhausting the land. The problem could be solved by means of linear programming (LP). This problem, however, seem to get very large as the number of crops as well as the number of years over which the problem is solved is increased. By assuming that the influence of crops is only for three years and by restricting the number of years over which the problem is solved the problem is greatly reduced. If we look at the dual of the problem we find a further reduction. The solution of the dual problem also leads to the formulation of strategies. If we formulate the problem by means of the above mentioned strategies the problem reduces to a linear programming problem with only one constraint (which is the knapsack problem). The solution of this knapsack problem with help of a little game theory is then used in a computer program to assist farmers in deciding which crops to plant.