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(5) Let a > 0 and let Cube(a) := {(x1, x2, X3, X4) € R4 | 0 ≤ X1, X2, X3, x4 ≤ a} be the cube in 4 dimensions whose sides all have length a. Conside the LPP of maximizing the cost function z = 2x₁ + 0x2 + 2x3 + 4x4 over the feasible set Cube(a) (a) Use the Simplex method to solve this LPP. What is the optimal BFS? (b) Indicate the path taken by the Simplex algorithm. That is list all the BFS correspond- ing to each of the tableau in Simplex. (c) At the optimal BFS you found in part (a), compute all the basic directions D, and show that the reduced costs c; are all non-positive.

(5) Let a > 0 and let Cube(a) := {(x1, x2, X3, X4) € R4 | 0 ≤ X1, X2, X3, x4 ≤ a} be the cube in 4 dimensions whose sides all have length a. Conside the LPP of maximizing the cost function z = 2x₁ + 0x2 + 2x3 + 4x4 over the feasible set Cube(a) (a) Use the Simplex method to solve this LPP. What is the optimal BFS? (b) Indicate the path taken by the Simplex algorithm. That is list all the BFS correspond- ing to each of the tableau in Simplex. (c) At the optimal BFS you found in part (a), compute all the basic directions D, and show that the reduced costs c; are all non-positive.

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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(5) Let a > 0 and let Cube(a) := {(x1, x2, X3, X4) € R4 | 0 ≤ X1, X2, X3, x4 ≤ a} be the cube in 4 dimensions whose sides all have length a. Conside the LPP of maximizing the cost function z = 2x₁ + 0x2 + 2x3 + 4x4 over the feasible set Cube(a) (a) Use the Simplex method to solve this LPP. What is the optimal BFS? (b) Indicate the path taken by the Simplex algorithm. That is list all the BFS correspond- ing to each of the tableau in Simplex. (c) At the optimal BFS you found in part (a), compute all the basic directions D, and show that the reduced costs c; are all non-positive.
Transcribed Image Text:(5) Let a > 0 and let Cube(a) := {(x1, x2, X3, X4) € R4 | 0 ≤ X1, X2, X3, x4 ≤ a} be the cube in 4 dimensions whose sides all have length a. Conside the LPP of maximizing the cost function z = 2x₁ + 0x2 + 2x3 + 4x4 over the feasible set Cube(a) (a) Use the Simplex method to solve this LPP. What is the optimal BFS? (b) Indicate the path taken by the Simplex algorithm. That is list all the BFS correspond- ing to each of the tableau in Simplex. (c) At the optimal BFS you found in part (a), compute all the basic directions D, and show that the reduced costs c; are all non-positive.
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