In contrast with Noether theorem, 
we built up a new operative procedure 
for the derivation of conserved quantities 
and then applied it to the extremal problem 
for the integration under constraints in the space of state 
and control variables. 
In the problem, conserved quantities were constructed 
by imposing the homogeneities 
with respect to the state variables through control variables 
on  relating functions. 
The purpose of this paper is to release the control variables 
from the homogeneities and then construct 
such a conserved quantity in a similar procedure. 
The quantity is illustratively constructed in a economic model, 
with the aid of 
which optimal paths can be determined completely.