Explore BrainMass
Share

Kuhn Tucker conditions

This content was STOLEN from BrainMass.com - View the original, and get the already-completed solution here!

Help to clarify matrices, Jacobian, quasi-concavity, Hessian, and Kuhn-Tucker conditions is provided.

1. (a) Solve the problem of minimizing x2 - 4x + 1 subject to x4 - 1 ≤ 0.

(b) Solve the problem of maximizing ƒ(x) = x subject to g(x) = x4 if x ≤ 0, 0 if x Є [0, 1], (x-1)4 if x ≥ 1. Explain why the Kuhn-Tucker conditions are inapplicable in this case.

© BrainMass Inc. brainmass.com October 24, 2018, 5:28 pm ad1c9bdddf
https://brainmass.com/economics/principles-of-mathematical-economics/kuhn-tucker-conditions-11407

Attachments

Solution Preview

please refer to the attachment.

1. (a) Solve the problem of minimizing x2 - 4x + 1 subject to x4 - 1 ≤ 0.

The Lagrangian Equation: (let b>0)
L= x2 - 4x + 1+ b(x4 - 1)
First Order Condition:
dL/dx=2x-4+4b x3 =0 (1)

Kuhn-Tucker condition:
b>=0, x4 - 1 ≤ 0
b( x4 - 1) = 0

if b=0, then from (1),we know x=2
but ...

Solution Summary

Kuhn Tucker conditions are described.

$2.19
See Also This Related BrainMass Solution

Jacobian, quasi-concavity, Hessian, Kuhn-Tucker conditions

How to apply matrices, Jacobian, quasi-concavity, Hessian, Kuhn-Tucker conditions?

View Full Posting Details