Consider the following LPP: maximize subject to ax₁ + 1x₂ -x1+x₂ ≤2 1 2x1 + x₂ ≤ 3 X1, X20 (a) For which values of a does this LPP have an optimal solution? Hint: draw the feasible set and consider the direction of the cost vector (a, 1). -³. (b) Solve this LPP graphically in the case when a = - (c) Use the Simplex method to solve this problem when a = -3. (d) Use the Simplex method to solve this problem when a = 1. Hint: does the LPP have an optimal solution in this case?
Consider the following LPP: maximize subject to ax₁ + 1x₂ -x1+x₂ ≤2 1 2x1 + x₂ ≤ 3 X1, X20 (a) For which values of a does this LPP have an optimal solution? Hint: draw the feasible set and consider the direction of the cost vector (a, 1). -³. (b) Solve this LPP graphically in the case when a = - (c) Use the Simplex method to solve this problem when a = -3. (d) Use the Simplex method to solve this problem when a = 1. Hint: does the LPP have an optimal solution in this case?
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 37CR
Related questions
Question
![(1) Consider the following LPP:
maximize
subject to
ax1 + 1x₂
-x₁ + x₂ ≤ 2
1
-X1 + X₂ ≤ 3
X1, X20
(a) For which values of a does this LPP have an optimal solution? Hint: draw the feasible
set and consider the direction of the cost vector (a, 1).
(b) Solve this LPP graphically in the case when a = -³.
3
3
(c) Use the Simplex method to solve this problem when a =
(d) Use the Simplex method to solve this problem when a = 1. Hint: does the LPP have
an optimal solution in this case?
4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffcda8012-1a8a-4b8e-b573-f51b0ed62e73%2F85398430-42ae-401d-9395-e55bee646e24%2Fxh3xc4_processed.png&w=3840&q=75)
Transcribed Image Text:(1) Consider the following LPP:
maximize
subject to
ax1 + 1x₂
-x₁ + x₂ ≤ 2
1
-X1 + X₂ ≤ 3
X1, X20
(a) For which values of a does this LPP have an optimal solution? Hint: draw the feasible
set and consider the direction of the cost vector (a, 1).
(b) Solve this LPP graphically in the case when a = -³.
3
3
(c) Use the Simplex method to solve this problem when a =
(d) Use the Simplex method to solve this problem when a = 1. Hint: does the LPP have
an optimal solution in this case?
4
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