On LP Sensitivity Analysis For each of the following two LP models, respond to the following questions using graphic tools and algebraic methods only: a) Identify the constraints that are binding and the ones that are not binding. b) Identify if any constraint is redundant (i.e., is not needed to delineate the feasibility region) c) Find the range of optimality of both of the objective function coefficients d) Find the shadow prices of each of the constraints e) Compute the amount by which the objective function changes, if the right-hand side of one of the constraints increases by 8%. Model 1: Maximize f = 4x + 7y subject to the following constraints: x+2y≤7 5x+3ys12 y≤3 x and y are non-negative Model 2 Maximize f = 7x + 5y subject to the following constraints: 3x + 4y < 24 2x + 1y ≤ 10 x ≥ 1 y ≤ 5 x and y are non-negative
On LP Sensitivity Analysis For each of the following two LP models, respond to the following questions using graphic tools and algebraic methods only: a) Identify the constraints that are binding and the ones that are not binding. b) Identify if any constraint is redundant (i.e., is not needed to delineate the feasibility region) c) Find the range of optimality of both of the objective function coefficients d) Find the shadow prices of each of the constraints e) Compute the amount by which the objective function changes, if the right-hand side of one of the constraints increases by 8%. Model 1: Maximize f = 4x + 7y subject to the following constraints: x+2y≤7 5x+3ys12 y≤3 x and y are non-negative Model 2 Maximize f = 7x + 5y subject to the following constraints: 3x + 4y < 24 2x + 1y ≤ 10 x ≥ 1 y ≤ 5 x and y are non-negative
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.8: Linear Programming
Problem 40E
Related questions
Question
![On LP Sensitivity Analysis
For each of the following two LP models, respond to the following questions using graphic tools
and algebraic methods only:
a) Identify the constraints that are binding and the ones that are not binding.
b) Identify if any constraint is redundant (i.e., is not needed to delineate the feasibility
region)
c) Find the range of optimality of both of the objective function coefficients
d) Find the shadow prices of each of the constraints
e) Compute the amount by which the objective function changes, if the right-hand side of
one of the constraints increases by 8%.
Model 1:
Maximize f = 4x + 7y subject to the following constraints:
x+2y≤7
5x+3ys12
y≤3
x and y are non-negative
Model 2
Maximize f = 7x + 5y subject to the following constraints:
3x + 4y < 24
2x + 1y ≤ 10
x ≥ 1
y ≤ 5
x and y are non-negative](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fadec6c6e-501b-48cc-a2bc-9a336b200c25%2F83f836eb-56fd-4450-ac8d-31ba45e75410%2F32637fo_processed.png&w=3840&q=75)
Transcribed Image Text:On LP Sensitivity Analysis
For each of the following two LP models, respond to the following questions using graphic tools
and algebraic methods only:
a) Identify the constraints that are binding and the ones that are not binding.
b) Identify if any constraint is redundant (i.e., is not needed to delineate the feasibility
region)
c) Find the range of optimality of both of the objective function coefficients
d) Find the shadow prices of each of the constraints
e) Compute the amount by which the objective function changes, if the right-hand side of
one of the constraints increases by 8%.
Model 1:
Maximize f = 4x + 7y subject to the following constraints:
x+2y≤7
5x+3ys12
y≤3
x and y are non-negative
Model 2
Maximize f = 7x + 5y subject to the following constraints:
3x + 4y < 24
2x + 1y ≤ 10
x ≥ 1
y ≤ 5
x and y are non-negative
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