Question 1: Simplex method. Consider the following LP problem: (b) (a) max s. t. x1x2 + x3 +3 x1x2 + 4x3 ≤ 0 x1 - x₂ = -1 x₁ + x3 ≥ −2 x₁ free, x2 ≥ 4,03 ≥ 0. Transform the given problem into an equivalent minimization LP problem in standard form. Hint: There are many ways of doing this. Try to obtain one with as few variables and constraints as possible in order to have fewer computations in the next steps. In particular, you may want to replace variable x2 with the new variable x2 = x2 − 4. Find a basic feasible solution of the LP problem obtained in (a) using Phase I of the two-phase simplex method. (c) Find an optimal basic feasible solution of the LP problem obtained in (a) using Phase II of the two-phase simplex method.
Question 1: Simplex method. Consider the following LP problem: (b) (a) max s. t. x1x2 + x3 +3 x1x2 + 4x3 ≤ 0 x1 - x₂ = -1 x₁ + x3 ≥ −2 x₁ free, x2 ≥ 4,03 ≥ 0. Transform the given problem into an equivalent minimization LP problem in standard form. Hint: There are many ways of doing this. Try to obtain one with as few variables and constraints as possible in order to have fewer computations in the next steps. In particular, you may want to replace variable x2 with the new variable x2 = x2 − 4. Find a basic feasible solution of the LP problem obtained in (a) using Phase I of the two-phase simplex method. (c) Find an optimal basic feasible solution of the LP problem obtained in (a) using Phase II of the two-phase simplex method.
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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Transcribed Image Text:Question 1: Simplex method.
Consider the following LP problem:
(b)
(a)
max
s. t.
x1 - x₂ + x3 +3
x1 - x2 + 4x3 ≤ 0
X1 X₂ = −1
x1 + x3 ≥ −2
x₁ free, x₂ ≥ 4,03 ≥ 0.
Transform the given problem into an equivalent minimization LP problem in standard
form.
Hint: There are many ways of doing this. Try to obtain one with as few variables and constraints
as possible in order to have fewer computations in the next steps. In particular, you may want to
replace variable x2 with the new variable x2 = x2 - 4.
Find a basic feasible solution of the LP problem obtained in (a) using Phase I of the
two-phase simplex method.
(c)
Find an optimal basic feasible solution of the LP problem obtained in (a) using Phase II
of the two-phase simplex method.
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