1. A) An automobile company sells 2 tires for every one frame. Now the demand function for tire is t=189 - P and demand function for frame f-180 - Pr and firm's cost function is C=3t2 + 3f2 + 3tf + 570 now use the Lagrange Multiplier Method of constrained optimization to optimize the profit. b) Now use the Bordered Hessian method to show that all the optimal values that you find in (a) maximize the profit. c) Define the significance of Lagrange Multiplier in optimization using this context. What is the other name of Lagrange Multiplier? Please briefly discuss how it will affect a firm's decision in this context? (Hint: is there any constant in your constraint?)

ENGR.ECONOMIC ANALYSIS
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ISBN:9780190931919
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Chapter1: Making Economics Decisions
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1. A) An automobile company sells 2 tires for every one frame. Now the demand function
for tire is
3
t=189 - P and demand function for frame f-180 – Pf and firm's cost function is
C=3t2 + 3f2 + 3tf + 570 now use the Lagrange Multiplier Method of constrained
optimization to optimize the profit.
b) Now use the Bordered Hessian method to show that all the optimal values that you find
4
in (a) maximize the profit.
c) Define the significance of Lagrange Multiplier in optimization using this context. What
is the other name of Lagrange Multiplier? Please briefly discuss how it will affect a firm's
decision in this context? (Hint: is there any constant in your constraint?)
Transcribed Image Text:1. A) An automobile company sells 2 tires for every one frame. Now the demand function for tire is 3 t=189 - P and demand function for frame f-180 – Pf and firm's cost function is C=3t2 + 3f2 + 3tf + 570 now use the Lagrange Multiplier Method of constrained optimization to optimize the profit. b) Now use the Bordered Hessian method to show that all the optimal values that you find 4 in (a) maximize the profit. c) Define the significance of Lagrange Multiplier in optimization using this context. What is the other name of Lagrange Multiplier? Please briefly discuss how it will affect a firm's decision in this context? (Hint: is there any constant in your constraint?)
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