Definition
Interpretation of Lagrange multiplier: marginal unit of the objective change per marginal unit of increase in the right-hand side of the constraint.
For example, if the constraint is income, the Lagrange multiplier shows the marginal utility of income.
Unit of Lagrange multiplier: unit of objective function / unit of constraint.
Sign of Lagrange multiplier:
- Relationship of constraint:
, maximizing objective: + - Relationship of constraint: , minimizing objective: -
- Relationship of constraint:
, minimizing objective: + - Relationship of constraint: , maximizing objective: -
- Relationship of constraint: =, maximizing or minimizing objective: ?
Note: if the program is not strict, I should write non-negative instead of +.
Consider the case
minimize F(x), subject to 
Write the Lagrange: 
FOC:
