We present in this paper an analytic stand by model for maximizing the discounted stream of utility from consumption when the rate of production is linear. We establish the model with the use of the concept of calculus of variation used to, solve Economic functional/variational problems of the form F t x t x t x t x t dt n t t z [ , ( ), ( ), ( ),..., ( ) ( )] 0 1 . The model generates solutions to problems of such linear systems when numerical values are supplied for all the parameters in the model.
