Consider the following linear programming problem: Мах 16x, + 14x2 + 15x3 + 50x4 2x, + 2x2 + 5x3 + 16x4 <800 3x, + 2x2 + 2x3 + 5x4 < 1000 2x1 + 1.2x2 + x3 + 4x4 < 680 X1, X2, X3, X4 20 s.t. : Using the simplex method, we obtain the following optimal tableau. The variables X5,X6, X7 are slack variables. RHS X5 X4 5 40 X7 d X1 X2 X3 X6 1 5.5 19 1.5 -1 200 1 -11 0.4 3.2 1 -1 a 0.2 -0.8 1 40 Find the unknown a through d. What is the optimal solution of the variables, and the corresponding optimal a) b) objective value? What is the optimal basis B and B-1? To obtain B-1, just find the unknown e through g in [1.5 =|-1 [0.2 -0.8 g] -1 B-1 1 f
Consider the following linear programming problem: Мах 16x, + 14x2 + 15x3 + 50x4 2x, + 2x2 + 5x3 + 16x4 <800 3x, + 2x2 + 2x3 + 5x4 < 1000 2x1 + 1.2x2 + x3 + 4x4 < 680 X1, X2, X3, X4 20 s.t. : Using the simplex method, we obtain the following optimal tableau. The variables X5,X6, X7 are slack variables. RHS X5 X4 5 40 X7 d X1 X2 X3 X6 1 5.5 19 1.5 -1 200 1 -11 0.4 3.2 1 -1 a 0.2 -0.8 1 40 Find the unknown a through d. What is the optimal solution of the variables, and the corresponding optimal a) b) objective value? What is the optimal basis B and B-1? To obtain B-1, just find the unknown e through g in [1.5 =|-1 [0.2 -0.8 g] -1 B-1 1 f
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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Transcribed Image Text:Consider the following linear programming problem:
Мах
16x, + 14x2 + 15x3
+ 50x4
2x1 + 2x2 + 5x3 + 16x4 < 800
3x1 + 2x2 + 2x3 + 5x4 <1000
2x1 + 1.2x2 + x3 + 4x4 < 680
X1, X2, X3, X4 20
s.t. :
Using the simplex method, we obtain the following optimal tableau. The variables x5 X6, x, are
slack variables.
RHS
X4
X3
b
X1
X2
X5
X6
2
X7
40
5
d
1
5.5
19
1.5
-1
200
1
-11
-1
1
0.4
3.2 0.2
-0.8
1
40
а)
b)
objective value?
Find the unknown a through d.
What is the optimal solution of the variables, and the corresponding optimal
What is the optimal basis B and B-1? To obtain B-1, just find the unknown e
through g in
[1.5
B-1 =-1
lo.2
-1
e
f
-0.8 g
1
d)
Is the optimal solution unique?
The profit of product 3 (c3) is changed from 15 to y. Please find the minimum y
so that the current optimal solution is still optimal.
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