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2? 
i.e., goods entering into the objective, and by maximizing a 
common scalar factor applied to these quantities (Figure 4). 
This problem can also be formulated in linear programming 
terms: One adds to the constraints (1) linear equalities expres- 
sing the prescribed ratios, and chooses as a maximand (2) the 
quantity of any one desired good, say. 
In convex programming the feasible set is defined by 
g(x, ..., x,)=20, 1=1, ..., m, 
where the g; are concave (1) functions, and the maximand 
U Ux, .... x, 
A 
$ 
concave function g(#y, ..., #,) is represented by a hypersurface 
£.%, ..., %,) in the space {y, x, ..., #,} that is never « below » any 
its chords (if the ++ direction is « up ») 
Koopmans - pag.