SECTION 9.6: Constrained Optimization

Graphical Approach: Maximizing Production Subject to a Budget Constraint

If f(x,y) has a global maximum or minimum on the constraint g(x,y) = c, it occurs at a point where the graph of the constraint is tangent to a contour of f, or at an endpoint of the constraint.

Analytical Approach: The Method of Legrange Multipliers

If P0 is a point satisfying the constraint g(x,y) = c,
the function f has a local maximum at P0 subject to the constraint if f(P0) >= f(P) for all points P near P0 satisfying the constraint.
the function f has a global maximum at P0 subject to the constraint if f(P0) >= f(P) for all points P satisfying the constraint.

In this particular reading, I was thoroughly confused by the Lagrangian multiplier and the Lagrangian function. I couldn not blog properly on the reading as I couldnt not understand the significance of most of it.

It is however relevant to economics because budget constraints play a crucial role in the development of a firm at microlevel or an entire country's economy at the macrolevel.