4. Reconsider the model in Problem 3 with objective function Maximize Z = C₁x₁ + ₂x₂, where C₁ ≥ 0, C₂ ≥ 0. Use the sensitivity analysis on the objective coefficients to answer the following questions. (a) Find the range of such that the optimal solution remains as (x₁, x₂) = (3,4). C₁ (b) Find the range of such that the optimal solution remains as (x₁,x₂) = (4,2). C₂ (c) Find the range of such that the optimal solution remains as (x₁, x₂) = (0,5). (d) If c₁ and c₂ are allowed to be negative, find the conditions on c₁ and C₂, and the range of such that the optimal solution remains as (x₁, x₂) = (4,0). C₂ Question 3 is given as follows: 3. Consider the following problem. Maximize Z = 3x₁ + 2x₂, subject to X1 ≤4 x₁ + 3x₂ ≤ 15 2x₁ + x₂ ≤ 10 (resource 1) (resource 2) (resource 3) and x₁ ≥ 0, x₂ ≥ 0, x3 ≥ 0. The optimal solution is (x₁, x₂) = (3,4) with Z* = 17. (a) Is any of these three constraints binding constraint? (b) Use graphical analysis to determine the shadow prices for the respective resources. 3
4. Reconsider the model in Problem 3 with objective function Maximize Z = C₁x₁ + ₂x₂, where C₁ ≥ 0, C₂ ≥ 0. Use the sensitivity analysis on the objective coefficients to answer the following questions. (a) Find the range of such that the optimal solution remains as (x₁, x₂) = (3,4). C₁ (b) Find the range of such that the optimal solution remains as (x₁,x₂) = (4,2). C₂ (c) Find the range of such that the optimal solution remains as (x₁, x₂) = (0,5). (d) If c₁ and c₂ are allowed to be negative, find the conditions on c₁ and C₂, and the range of such that the optimal solution remains as (x₁, x₂) = (4,0). C₂ Question 3 is given as follows: 3. Consider the following problem. Maximize Z = 3x₁ + 2x₂, subject to X1 ≤4 x₁ + 3x₂ ≤ 15 2x₁ + x₂ ≤ 10 (resource 1) (resource 2) (resource 3) and x₁ ≥ 0, x₂ ≥ 0, x3 ≥ 0. The optimal solution is (x₁, x₂) = (3,4) with Z* = 17. (a) Is any of these three constraints binding constraint? (b) Use graphical analysis to determine the shadow prices for the respective resources. 3
Practical Management Science
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ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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Question
![4. Reconsider the model in Problem 3 with objective function Maximize Z = C₁x₁ + ₂x₂, where
C₁ ≥ 0, C₂ ≥ 0. Use the sensitivity analysis on the objective coefficients to answer the following
questions.
(a) Find the range of 1, such that the optimal solution remains as (x₁,x₂) = (3,4).
C₂
(b) Find the range of
such that the optimal solution remains as (x₁, x₂) = (4, 2).
(c) Find the range of
such that the optimal solution remains as (x₁, x₂) = (0,5).
(d) If c₁ and c₂ are allowed to be negative, find the conditions on c₁ and C₂, and the range of
such that the optimal solution remains as (x₁, x₂) = (4,0).
C₂
Question 3 is given as follows:
3. Consider the following problem.
Maximize Z = 3x₁ + 2x₂,
subject to
X1
(resource 1)
<4
x₁ + 3x₂15
(resource 2)
2x₁ + x₂ 10 (resource 3)
and x₁ ≥ 0, x₂ ≥ 0, x3 ≥ 0.
The optimal solution is (x₁, x₂) = (3,4) with Z* = 17.
(a) Is any of these three constraints binding constraint?
(b) Use graphical analysis to determine the shadow prices
for the respective resources.
3
14](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2f2c4bd-bf4c-4a3b-a0a2-6333c3306a45%2F66dbfbe6-9fb0-42e4-a012-61502897af75%2Frxhfdx9a_processed.png&w=3840&q=75)
Transcribed Image Text:4. Reconsider the model in Problem 3 with objective function Maximize Z = C₁x₁ + ₂x₂, where
C₁ ≥ 0, C₂ ≥ 0. Use the sensitivity analysis on the objective coefficients to answer the following
questions.
(a) Find the range of 1, such that the optimal solution remains as (x₁,x₂) = (3,4).
C₂
(b) Find the range of
such that the optimal solution remains as (x₁, x₂) = (4, 2).
(c) Find the range of
such that the optimal solution remains as (x₁, x₂) = (0,5).
(d) If c₁ and c₂ are allowed to be negative, find the conditions on c₁ and C₂, and the range of
such that the optimal solution remains as (x₁, x₂) = (4,0).
C₂
Question 3 is given as follows:
3. Consider the following problem.
Maximize Z = 3x₁ + 2x₂,
subject to
X1
(resource 1)
<4
x₁ + 3x₂15
(resource 2)
2x₁ + x₂ 10 (resource 3)
and x₁ ≥ 0, x₂ ≥ 0, x3 ≥ 0.
The optimal solution is (x₁, x₂) = (3,4) with Z* = 17.
(a) Is any of these three constraints binding constraint?
(b) Use graphical analysis to determine the shadow prices
for the respective resources.
3
14
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