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+3y<12 y≤3 x and y are non-negative Model 2 Maximize f = 7x + 5y subject to the following constraints: 3x + 4y < 24 2x + 1y ≤ x ≥ 1 10
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+3y<12 y≤3 x and y are non-negative Model 2 Maximize f = 7x + 5y subject to the following constraints: 3x + 4y < 24 2x + 1y ≤ x ≥ 1 10
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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Please use graphic tools and algebric method to answer the question
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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