Answer 4,5,6 Consider the following optimization problem(P)min x1s.t. x² + ax ≤ 122 ≤1where 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 which3. (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.

IntroductionWe consider the optimization problem defined as:minx1 s.t. x12+αx22≤1 x2≤1where is a…

Answered: Consider the following optimization…

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

Related questions

Question

Answer 4,5,6

Expert Solution

Step 1: Question 4

Introduction

We consider the optimization problem defined as:

$\begin{array}{lll} min & x_{1} & s.t. & x_{1}^{2} + α x_{2}^{2} \leq 1 & x_{2} \leq 1 \end{array}$

where is a parameter. We aim to answer questions 4, 5, and 6 regarding the feasibility, boundedness, and infeasibility of the problem.

Analysis

Question 4: Feasibility of }

To check if is a feasible solution, we substitute these values into the constraints:

$x subscript 1 superscript 2 plus alpha x subscript 2 superscript 2 less or equal than 1$ becomes $1 squared plus alpha times 0 squared less or equal than 1$ , which simplifies to $1 less or equal than 1$ .
$x subscript 2 less or equal than 1$ becomes $0 less or equal than 1$ .

Both constraints are satisfied for any value of . Therefore, is a feasible solution for all .