Research on Crop Planting based on Linear Programming and Multiple Regression Functions

The purpose of this paper is to explore how to optimize crop planting strategies through linear programming and multiple regression functions to help rural revitalization and agricultural modernization. In the study, we consider a variety of factors such as crop planting seasons, plot types, and potential planting risks. By analyzing the crop suitability of different plots and combining constraints such as arable land area limitations and crop rotation requirements, we established a linear programming model with the objective of maximizing economic benefits. At the same time, for the two cases of stagnant and wasteful marketing and selling at a reduced price when the yield exceeds the expectation, binary decision variables are used to find the optimal solution. In addition, this paper uses multiple regression functions to predict the growth rate of sales of major crops such as corn and wheat and predicts the future price growth of edible mushrooms through a gray prediction model (GM (1,1)). In the course of the study, we also discuss the impact of extreme weather due to monsoon climate in the northern region and give the optimal planting scheme based on these perturbation factors. Through gray correlation analysis, this paper further explores the correlation coefficients between planting cost and selling price relative to expected sales volume and combines the principles of complementarity and substitutability to derive the highest yielding planting strategy. Finally, the stability of the model is verified by sensitivity analysis, and its adaptability in other agricultural scenarios is explored.