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2. Consider the linear program below and the optimal simplex tableau. Maximize 2x1+6x2+8x3 Subject to r1+x2-2x3 < 10 -x1+x2+2x3 < 20 xi+x2+x3= 10 X; > 0, i = 1,2, 3. X4 X5 Y1 RHS BV 1 1 30 X4 1/3 1/3 2/3 M+4 1 10 1 ½ 0 0 0 2 80 + OBJ Here yı is artificial variable in constraint 3. (a) Introduce a new variable x6 with cost coefficient 10 and constraint coefficients 1, 1, 1 and compute the new optimal solution, if any.

2. Consider the linear program below and the optimal simplex tableau. Maximize 2x1+6x2+8x3 Subject to r1+x2-2x3 < 10 -x1+x2+2x3 < 20 xi+x2+x3= 10 X; > 0, i = 1,2, 3. X4 X5 Y1 RHS BV 1 1 30 X4 1/3 1/3 2/3 M+4 1 10 1 ½ 0 0 0 2 80 + OBJ Here yı is artificial variable in constraint 3. (a) Introduce a new variable x6 with cost coefficient 10 and constraint coefficients 1, 1, 1 and compute the new optimal solution, if any.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.3: Systems Of Inequalities
Problem 19E
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2. Consider the linear program below and the optimal simplex tableau.
Maximize 2x1+6x2+8x3
Subject to x1+x2-2x3 ≤ 10
-x1+x2+2x3 ≤ 20
x1+x2+x3 = 10
xi ≥ 0, i = 1, 2, 3.


x1 x2 x3 x4 x5 y1 RHS BV
0 2 0 1 1 0 30 x4
0 2/3 1 0 1/3
1/3 10 x3
1 1/3 0 0 -1/3
2/3 0 x1
0 0 0 0 2 M+4 80 ⇐ OBJ
Here y1 is artificial variable in constraint 3.
(a) Introduce a new variable x6 with cost coefficient 10 and constraint coefficients 1, 1, 1 and compute the new optimal solution, if any.

(b) Delete variable x3 from the given tableau and obtain the new optimal solution, if exists.

2. Consider the linear program below and the optimal simplex tableau. Maximize 21+6x2+8x3 Subject to x1+x2-2x3 < 10 -x1+x2+2x3 < 20 X1+x2+x3 = 10 X; > 0, i = 1,2, 3. X2 X3 X4 Y1 RHS BV 1 1 30 X4 2/3 1 1/3 0 1/3 0 -/3 2/3 М+4 1/3 10 X3 1 2 80 + OBJ Here yı is artificial variable in constraint 3. (a) Introduce a new variable x, with cost coefficient 10 and constraint coefficients 1, 1, 1 and compute the new optimal solution, if any. (b) Delete variable x3 from the given tableau and obtain the new optimal solution, if exists. 2.
Transcribed Image Text:2. Consider the linear program below and the optimal simplex tableau. Maximize 21+6x2+8x3 Subject to x1+x2-2x3 < 10 -x1+x2+2x3 < 20 X1+x2+x3 = 10 X; > 0, i = 1,2, 3. X2 X3 X4 Y1 RHS BV 1 1 30 X4 2/3 1 1/3 0 1/3 0 -/3 2/3 М+4 1/3 10 X3 1 2 80 + OBJ Here yı is artificial variable in constraint 3. (a) Introduce a new variable x, with cost coefficient 10 and constraint coefficients 1, 1, 1 and compute the new optimal solution, if any. (b) Delete variable x3 from the given tableau and obtain the new optimal solution, if exists. 2.
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