A nonlinear transportation model: a step-by-step solution

The model has linear restraints and a functional, to be maximised, consisting of linear first-order interactions of variables. General applications of the model are stated. It is shoran that a direct solution is not generally possible, but iterative procedures, analogous to the 'Transportation' technique are developed both for integer and non-integer non-negative variables. A Tableau procedure is given, with suitable checks, to enable a solution to be systematically obtained:, and finally a numerical example is treated.