Some Types of Dual Decision Making

     Every decision making has its duality decision making.However,different types of decision making may have different dual decision making.This paper classifies them into two types:
     1.Unconstraint decision making's duality
     The duality decision making of profit maximization is the decision making of deficit minimization.
     2.Constraint Decision making's duality
     It can be classified into two subclasses , one of which has the common decision making variables and the other of which has different variables.
     (1)duality decision making have the same variables
      for example:
      primal decision making: the utility maximization decision making subject to the constant expenditure which can be formulated as following:
      Max U=U(X1,X2) s.t. P1X1+P2X2=m,
      Dual decision making:the expenditure minimization decision making subject to the constant utility which can be formulated as following:
      Min E=P1X1+P2X2,s.t. U(X1,X2)=u
      there u is a parameter which indicates the utility level that consumer want to reach.
     In these dual decision making,they have the same varibles of decision making.
   (2)Duality decision making have different variables
       This case mainly occur in linear programming,for example:
      Primal decision making: Maximization of profit with respect to products combination of a firm
           Max profit=2X1+3X2  
            s.t.          3X1+5X2<=120
                          2X1+X2<=60
                          X1、X2>=0
      Duality decision making: Minimization of return of the resources
           Min sale price=120Y1+60Y2
               s.t.       3Y1+2Y2>=2
                           5Y1+Y2>=3
                           Y1,Y2>=0
        Y1 is the shadow price(shadow value) of the first resource in the primal decision making,and Y2 is the shadow price of the second resource.

     I wonder wheher some other types of duality decision making rather than the above existing in economics or maths.If you are familiar with them,please tell me,thank you.