Answer 5,6,7,8
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Answer 5,6,7,8
Transcribed Image Text:Consider the following optimization problem
(P)
min x1
s.t. x² + ax ≤1
22 ≤1
where a is a parameter (i.e., it is not a variable).
Answer the following questions.
1. Obtain an optimal solution of (P) graphically when a = 1.
2. Obtain an optimal solution of (P) graphically when a = -1.
Find all the values of a (if any) for which
3. (1,0) is a feasible solution to (P).
4. (0,1) is a feasible solution to (P).
5. Problem (P) is unbounded.
6. Problem (P) is infeasible.
7. Problem (P) can be written as a linear optimization model.
8. Problem (P) has multiple optimal solutions.
Expert Solution
Step 1: 5. Problem (ρ) is unbounded:
An optimization problem is unbounded if there exists a feasible solution, but the objective function can be improved indefinitely. In the context of linear programming, if problem (ρ) is unbounded, then the dual problem is not feasible. However, in this case, the problem (ρ) is not a linear programming problem because of the quadratic constraint x12 + αx22 ≤ 1. Therefore, it's not straightforward to determine if it's unbounded without additional information or analysis.
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