Optimization and Lagrangian. Partial Derivative Concept Consider a demand function dependent of both price and advertising Q = f(P,A) Analyzing a multivariate.

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Presentation transcript:

Optimization and Lagrangian

Partial Derivative Concept Consider a demand function dependent of both price and advertising Q = f(P,A) Analyzing a multivariate function often requires considering the independent variable impact on the dependent variable, all else equal. The partial derivative can be useful with this type of analysis. Consider the function

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Optimization and Lagrangian Lagrangian Multipliers (constrained optimization) by subtraction multiplying by 7 then by adding which is and by substitution which is is then

Optimization and Lagrangian Lagrangian Multipliers (constrained optimization) Given it takes 4 fours of labor to produce output with only 300 hours available. which is is then