Introduction: A constrained extremum problem is given by
Remark: The method of Lagrange results in $\lambda$, which can be seen as a shadow price. This shadow price gives an indication of the increase of the object function when the restriction is weakened by increasing $k$ by one unit.
Example: Consider the following constrained extremum problem (see Example (film)).
- Optimize $z(x,y)$
- Subject to $g(x,y)=k$
- Where $x \in D_1$, $y \in D_2$
Remark: The method of Lagrange results in $\lambda$, which can be seen as a shadow price. This shadow price gives an indication of the increase of the object function when the restriction is weakened by increasing $k$ by one unit.
Example: Consider the following constrained extremum problem (see Example (film)).
- Maximize $z(x,y)=2xy+3y$
- Subject to $4x+y=10$
- Where $x,y>0$