Regarding the cattle industry in Greece, the main concern is to promote self-sufficiency, in the context of minimizing imports, by increasing the output. Since in multi-product farms, there is a close interdependence regarding production response and changes in relative profitability, the problem set is to determine the optimal price policy for attaining some pro-assigned levels of production without reducing the stocks. In this context an optimal control problem has been formulated for the purpose of deriving the optimum structure of the relative farm prices. The control problem has been solved by applying a procedure which utilizes some useful properties of the generalized inverse. The method has been found to be quite efficient, for a certain class of optimal control problems, when compared with other routine methods.