The family, as a socially balanced system, possesses the functions of social information communication and social resource conversion. From the perspective of the family system as a provider of educational resources, the input of various forms of resources into the family environment either helps parents to teach their children, helps them to learn, or is detrimental to the healthy growth of their children. In this paper, based on the nonlinear model of the static resource-opportunity allocation problem study, the objective constraints are added to establish a linear programming model. The column enumeration method is used to solve the linear programming, while the sensitivity of the linear programming is analyzed by pairwise test. On the basis of the random initial solution, a multilayer transportation algorithm is designed as the initial solution to further reduce the time of enumerating columns and complete the construction of the solution framework for the resource-opportunity allocation problem. The model is used to solve the problem of the distribution of socio-economic resources to educational opportunities between “two-child” and “one-child” families. The results show that the socio-economic resources of different families have different opportunities for children’s education, and there are significant differences between different types of “two-child” families in the three aspects of parent-child relationship satisfaction, feelings of parenting, and interpersonal evaluation of the child, with the F-values of 5.265, 4.859, and 5.136, respectively, with a p<0.01. The “last-child advantage” in children's education is related to the number of years of education of the fathers. In the 1949-1969 generation, the average number of years of education of the fathers was only 6.763, while in the 1970-1990 generation, the average number of years of education of the fathers increased to 8.685, and the cultural level of the family as a whole improved significantly, and the mechanism of resource constraints on the cultural level of the family began to take effect. The resource constraint mechanism at the cultural level is beginning to take effect.