For a quasi-concave function f and a quasi-convex function g on <∼nab22Å-, the paper studies the two following problems: (M) maxf(x) for x∈&λτ;∼nab22<Å- and g(x)∈b; and (m) ming(x) for x∈&λτ;∼nab22<Å- and f(x)∈c. It also establishes a duality theorem. These results can be used to see the analogy between the classical economic theories of the consumer and of the firm.
