The following is a LPP: Max Z- 5X1• 7X2+ 6X3 (Hundreds of dollars $) s.t: 3X1 4X2 2X3 - 90 X1+ 2X2 + X3 <- 47.2 X1+ 3X2 + X3 <- 30 X1,X2,X3>-0 (production capacity; hours) (warehouse capacity: hundreds of sq. ft.) (demand for 6 oz. glasses; hundreds of cases) The optimal solution to the model as follows Basis CB 6X1 7X2 6X3 S1 $2 S3 RHS X2 S1 X1 0. 0.5 1 -0.6 1. 10 -1 -3 10 -1 10 1. 1.5 -1.5 5. 8.5 0. 2. 120 C-z 0. -2.5 What effect on the optimal solution (value of Z) ,if we change b2 from 47.2 to 58.9 ?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
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QUESTION 1o
The following is a L.P.P:
Max Z- 5X1 + 7X2 + 6X3 (Hundreds of dollars $)
s.t:
3X1 + 4X2 + 2X3 <- 90
X1+ 2X2 + X3 <- 47.2
X1+ 3X2 + X3 <- 30
X1,X2,X3>-0
(production capacity; hours) (warehouse capacity: hundreds of sq. ft.) (demand for 6 oz. glasses; hundreds of cases)
The optimal solution to the model as follows:
Basis
Св
5X1
7X2
6X3
S1
S3
1.
$2
RHS
X2
S1
X1
1
0.5
1
-0.5
10
-1
-3
10
-1
10
8.5
1.5
120
C-Z
-2.5
-1.5
-2
What effect on the optimal solution (value of Z) ,if we change b2 from 47.2 to
58.9 ?
Transcribed Image Text:QUESTION 1o The following is a L.P.P: Max Z- 5X1 + 7X2 + 6X3 (Hundreds of dollars $) s.t: 3X1 + 4X2 + 2X3 <- 90 X1+ 2X2 + X3 <- 47.2 X1+ 3X2 + X3 <- 30 X1,X2,X3>-0 (production capacity; hours) (warehouse capacity: hundreds of sq. ft.) (demand for 6 oz. glasses; hundreds of cases) The optimal solution to the model as follows: Basis Св 5X1 7X2 6X3 S1 S3 1. $2 RHS X2 S1 X1 1 0.5 1 -0.5 10 -1 -3 10 -1 10 8.5 1.5 120 C-Z -2.5 -1.5 -2 What effect on the optimal solution (value of Z) ,if we change b2 from 47.2 to 58.9 ?
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