This paper presents the contradiction between the objective function of the original question and the result based on the principle of optimal resource allocation

one of the basic princriples of modern economics

that the same kind of resources will bring about the same marginal output and price. Therefore

"marginal out puts are equivalent everywhere" should not have been the result based on the principle. The paper also points out that the independence of variables is in conflict with the intrinsic relation of natural resouces

and that the principle should have had limitations on tatal demands. As a result

a pen-nonlinear programming model is introduced. and finally

the fastest approach to achieving tatal utility goal is discussed on the principle of optimal resource allocation.