Solving the production cost minimization problem with the Cobb – Douglas production function without the use of derivatives

In this paper, we propose a new original method to solve the production cost minimization problem with Cobb-Douglas production function by using the weighted arithmetic-geometric-mean inequality (weighted AM-GM inequality). Instead of using derivatives or the Lagrange multiplier method, the minimum costs and global minimizers in the case of the Cobb-Douglas production function are derived in the direct way. The result is first derived for the case of two inputs and then generalized for the problem with n inputs.