In minimization problems, dual values (or shadow prices) represent the change in the objective function value for a one-unit increase in the right-hand side of a constraint. A positive dual value indicates that increasing the resource associated with that constraint will reduce the overall cost of the objective function, making it valuable. Conversely, a dual value of zero suggests that increasing the resource has no impact on the minimum cost. These values help prioritize which constraints can provide the most significant cost savings if resources are increased.