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Question: Help Needed: Solving for Optimal 𝑝 1 ∗ ​ under Multiple Bound

Question:Help Needed: Solving for Optimal 𝑝 1 ∗ ​ under Multiple Bound

Andiguys 65 Maple 2019
optimization duplicate-question constraints
June 05 2025
0

I'm working on an optimization problem involving a single decision variable p1, subject to four inequality constraints:

  • Two upper bound constraints:

    p1 < b1,p1 < b2

  • Two lower bound constraints:

    c1 ≤ p1,c2 ≤ p1

Effectively, the feasible region for p1 is:

max⁡(c1,c2)  ≤  p1  ≤  min⁡(b1,b2)

I have already formulated the Karush-Kuhn-Tucker (KKT) conditions for this setup, and now I'm trying to determine:

  1. The optimal value p1∗​

  2. The corresponding feasibility conditions

  3. A case-wise breakdown depending on which constraints are active or inactive


Sheet:  Q_P1_Optimum_condition.mw
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