This paper develops an extended newsboy model and presents a formulation for this model.This new model has solved the budget contained multi-product newsboy problem with the reactive production.This model can be used to describe the status of entrepreneurial network construction.We use the Lagrange multiplier procedure to deal with our problem,but it is too complicated to get the exact solution.So we introduce the homotopy method to deal with it.We give the flow chart to describe how to get the solution via the homotopy method.We also illustrate our model in both the classical procedure and the homotopy method.Comparing the two methods,we can see that the homotopy method is more exact and efficient.