The following linear programming problem described the manufacturing two products (X1 & X2) by using two raw materials (R1 & R2); Max. Z= 3X1 + 4X2 Subject to: 2X1 + 3X2 1200 (Constraint of raw material R1) 2X1 + X2s 1000 (Constraint of raw material R2) X2s 200 (Demand for product X2) X1 X2 2 0 1- By using the Algebraic Analysis, find whether a change in the right-hand side for constraint of raw material R1, (1200), and the current basis remains optimal. 2- Change this linear programming model to Dual Problem Model, and find the values of the variables and W by using the optimal simplex tableau which shown below.

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1:03 O 69%
O X ll 100 Jo
The following linear programming
problem described the
manufacturing two products (X1 &
X2) by using two raw materials (R1 &
R2);
Маx. Z- 3X1 +
4X2
Subject to:
(Constraint of raw material R1)
2X1 + 3X2 < 1200
2X1 + X2< 1000
(Constraint of raw material R2)
X2s 200
(Demand for product X2)
X1 X2 2 0
1-
By using the Algebraic
Analysis, find whether a change in
the right-hand side for constraint of
raw material R1, (1200), and the
current basis remains optimal.
2-
Change this linear
programming model to Dual Problem
Model, and find the values of the
variables and W by using the optimal
simplex tableau which shown below.
B.V. X1 X2
S2
S3
K
X1
1
0 - 1/4 3/4
450
X2
1
1/2 - 1/2 0
100
S3
-1/2 1/2
1
200
Transcribed Image Text:1:03 O 69% O X ll 100 Jo The following linear programming problem described the manufacturing two products (X1 & X2) by using two raw materials (R1 & R2); Маx. Z- 3X1 + 4X2 Subject to: (Constraint of raw material R1) 2X1 + 3X2 < 1200 2X1 + X2< 1000 (Constraint of raw material R2) X2s 200 (Demand for product X2) X1 X2 2 0 1- By using the Algebraic Analysis, find whether a change in the right-hand side for constraint of raw material R1, (1200), and the current basis remains optimal. 2- Change this linear programming model to Dual Problem Model, and find the values of the variables and W by using the optimal simplex tableau which shown below. B.V. X1 X2 S2 S3 K X1 1 0 - 1/4 3/4 450 X2 1 1/2 - 1/2 0 100 S3 -1/2 1/2 1 200
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