(d) What is the optimal solution of the original problem that you have obtained? What is the optimal cost of the original problem? (e) Is the optimal solution unique? If yes, why? If not, give a different optimal solution.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Please just solve for the questions (d) and (e)

Please just solve for the questions (d) and (e)

 

I will be very very appreciate!!

(d)
What is the optimal solution of the original problem that you have obtained? What is
the optimal cost of the original problem?
(e)
Is the optimal solution unique? If yes, why? If not, give a different optimal solution.
Transcribed Image Text:(d) What is the optimal solution of the original problem that you have obtained? What is the optimal cost of the original problem? (e) Is the optimal solution unique? If yes, why? If not, give a different optimal solution.
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.
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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