LAGRANGE MULTIPLIER

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# LAGRANGE MULTIPLIER - PowerPoint PPT Presentation

LAGRANGE MULTIPLIER. BY ENI SUMARMININGSIH, SSI, MM. Constained Optimization. “Constrained Optimization” involves the optimization of a process subject to constraints. Constraints have two basic types — Equality Constraints -- some factors have to equal constraints

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### LAGRANGE MULTIPLIER

BY ENI SUMARMININGSIH, SSI, MM

Constained Optimization

“Constrained Optimization” involves the optimization of a process subject to constraints.

Constraints have two basic types

— Equality Constraints -- some factors have to equal constraints

— Inequality Constraints -- some factors have to be less less than or greater than the constraints (these are “upper” and “lower” bounds

Equality Constraints

Subject to (s.t.):

Total costs = Budget = p1x1 + p2x2

APPROACH

In this case, transform optimization of a

“constrained” situation to optimization of

“unconstrained” situation

Shadow Price is the Rate of change of objective function per unit change of constraint

This is meaning of Lagrangean multiplier

SOAL -SOAL

1. Minimize f(x) = +

S.t.

2. Minimize +

s.t

3. Minimize

s.t.