(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.

Intermediate Algebra

10th Edition

ISBN:9781285195728

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter9: Functions

Section9.CR: Review Problem Set

Problem 37CR: A garden has 60 yards of fencing and wants to enclose a rectangular garden that requires fencing...

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