  We study a new non-classical class of variational problems that is motivated
by some recent research on the non-linear revenue problem in the field of
economics. This class of problem can be set up as a maximising problem in the
Calculus of Variations (CoV) or Optimal Control. However, the state value at
the final fixed time, y(T), is a priori unknown and the integrand is a function
of the unknown y(T). This is a non-standard CoV problem. In this paper we apply
the new costate boundary conditions p(T) in the formulation of the CoV problem.
We solve some sample examples in this problem class using the numerical
shooting method to solve the resulting TPBVP, and incorporate the free y(T) as
an additional unknown. Essentially the same results are obtained using symbolic
algebra software.
