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Consider the following problem: Maximize W(x,y) = 2ln(x) + c.ln(y) subject to the constraints: x ≥ 0, y ≥ 0, x + y ≤ 15, 2x+y ≤ 20. Here c is a positive parameter.   Set up the Lagrangean for this problem. For the specific case where c = 1 solve the maximization problem.

Consider the following problem: Maximize W(x,y) = 2ln(x) + c.ln(y) subject to the constraints: x ≥ 0, y ≥ 0, x + y ≤ 15, 2x+y ≤ 20. Here c is a positive parameter.   Set up the Lagrangean for this problem. For the specific case where c = 1 solve the maximization problem.

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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  1. Consider the following problem: Maximize W(x,y) = 2ln(x) + c.ln(y) subject to the constraints: x ≥ 0, y ≥ 0, x + y ≤ 15, 2x+y ≤ 20. Here c is a positive parameter.

 

  1. Set up the Lagrangean for this problem.
  2. For the specific case where c = 1 solve the maximization problem.
  3. For what values of c is the constraint 2x+y ≤ 20 non-binding at the optimum?

Derive the bordered Hessian for the case where 2x+y ≤ 20 is not binding and verify that your solution is a global maximum

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