Consider the following linear optimization model: (P) max s.t. x1 + 2x₂ -x1+x₂ ≤ 6 x12x2 ≤ 4 X1, X2 ≥ 0. 1. Determine all vertices and extreme rays of the feasible region of (P) by drawing its feasible region. 2. Using the extreme rays, argue that (P) is unbounded. 3. Put problem (P) in standard form. Find all basic solutions to this system; label them A, B, C, ... Indicate these solutions (using their labels) on the figure you drew in Part 1. 4. Use the simplex algorithm (starting from the basis composed of slack variables) to show that (P) is unbounded. When multiple variables are eligible to enter the basis, select the eligible variable with highest reduced cost. If multiple variables are eligible to leave the basis, select the eligible variable whose index is smallest. (When providing an answer to this problem, report (at least) the simplex dictionary obtained at each iteration, and state what variables are entering/leaving the basis.) 5. Represent the sequence of basic solutions you encountered during simplex on the figure you drew in Part 1.

Consider the following linear optimization model: (P) max s.t. x1 + 2x₂ -x1+x₂ ≤ 6 x12x2 ≤ 4 X1, X2 ≥ 0. 1. Determine all vertices and extreme rays of the feasible region of (P) by drawing its feasible region. 2. Using the extreme rays, argue that (P) is unbounded. 3. Put problem (P) in standard form. Find all basic solutions to this system; label them A, B, C, ... Indicate these solutions (using their labels) on the figure you drew in Part 1. 4. Use the simplex algorithm (starting from the basis composed of slack variables) to show that (P) is unbounded. When multiple variables are eligible to enter the basis, select the eligible variable with highest reduced cost. If multiple variables are eligible to leave the basis, select the eligible variable whose index is smallest. (When providing an answer to this problem, report (at least) the simplex dictionary obtained at each iteration, and state what variables are entering/leaving the basis.) 5. Represent the sequence of basic solutions you encountered during simplex on the figure you drew in Part 1.

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter12: Algebra Of Matrices

Section12.CR: Review Problem Set

Problem 35CR: Maximize the function fx,y=7x+5y in the region determined by the constraints of Problem 34.

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