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Consider the following problem: Minimize (x1 – 4)² + (x2 – 6)? subject to x2 2 xf X2 <4.

Consider the following problem: Minimize (x1 – 4)² + (x2 – 6)? subject to x2 2 xf X2 <4.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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help with exercise 3.45

[3.45] Consider the following problem: Minimize (x1 – 4)² + (x2 – 6)² - subject to x2 2 xí X2 <4. Write a necessary condition for optimality and verify that it is satisfied by the point (2, 4). Is this the optimal point? Why?
Transcribed Image Text:[3.45] Consider the following problem: Minimize (x1 – 4)² + (x2 – 6)² - subject to x2 2 xí X2 <4. Write a necessary condition for optimality and verify that it is satisfied by the point (2, 4). Is this the optimal point? Why?
Expert Solution
Step 1

In this question, we write the necessary condition for the optimality and verify it for the point(2,4)

the system is

minimize (x1-4)2+(x2-6)2 s.t.x2≥x12x2≤4

 

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