1. Consider the parametric linear programMaximize (4 + 4λ)x1+(4 + 8λ)x2+(8 + 4λ)x3Subject to x1+3x2-x3 ≤ 10-x1+x2+2x3 ≤ 152x1+x2+x3 ≤ 20xi ≥ 0, i = 1, 2, 3.An optimal simplex tableau of the LP for λ = 0 is given below.x1 x2 x3 x4 x5 x6 RHS BV0 17/5 0 1 3/5 -1/5 15 x40 3/5 1 0 2/51/5 10 x31 1/5 0 0 -1/52/5 5 x10 8/5 0 0 12/516/5 100 ⇐ OBJ(a) Compute the characteristic interval for the optimal basis and identify the slope of f(λ), the optimal objective function value as a function of λ, for λ belongs to this interval.(b) Compute the new optimal solution if the RHS vector is replaced by (10, 20, 30)T and λ = 0 1. Consider the parametric linear programMaximize (4+ 4X)x1+(4+8A)x2+(8+4X)x3Subject to 1+3x2-x3 < 10-x1+x2+2x3 < 152.01+x2+x3 < 20X; > 0, i = 1,2, 3.An optimal simplex tableau of the LP for = 0 is given below.X2X3 X4X6RHSBV0 17/5 03/31/50 8/5 03/5 -1/52/5 1/50 -1/5 2/50 2/5 16/5115X41101100 + OBJ(a) Compute the characteristic interval for the optimal basis and identify the slope off(A), the optimal objective function value as a function of A, for A belongs to thisinterval.(b) Compute the new optimal solution if the RHS vector is replaced by (10, 20, 30)7and A= 0

Name: 1. Consider the parametric linear programMaximize (4 + 4λ)x1+(4 + 8λ)x
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Description: 1. Consider the parametric linear programMaximize (4 + 4λ)x1+(4 + 8λ)x2+(8 + 4λ)x3Subject to x1+3x2-x3 ≤ 10-x1+x2+2x3 ≤ 152x1+x2+x3 ≤ 20xi ≥ 0, i = 1, 2, 3.An optimal simplex tableau of the LP for λ = 0 is given below.x1 x2 x3 x4 x5 x6 RHS BV0 17/5 0

Answered: 1. Consider the parametric linear…

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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1. Consider the parametric linear program

Maximize (4 + 4λ)x1+(4 + 8λ)x2+(8 + 4λ)x3
Subject to x1+3x2-x3 ≤ 10
-x1+x2+2x3 ≤ 15
2x1+x2+x3 ≤ 20
xi ≥ 0, i = 1, 2, 3.

An optimal simplex tableau of the LP for λ = 0 is given below.
x1 x2 x3 x4 x5 x6 RHS BV
0 17/5 0 1 3/5 -
1/5 15 x4
0 3/5 1 0 2/5
1/5 10 x3
1 1/5 0 0 -1/5
2/5 5 x1
0 8/5 0 0 12/5
16/5 100 ⇐ OBJ

(a) Compute the characteristic interval for the optimal basis and identify the slope of f(λ), the optimal objective function value as a function of λ, for λ belongs to this interval.

(b) Compute the new optimal solution if the RHS vector is replaced by (10, 20, 30)T and λ = 0

1. Consider the parametric linear program
Maximize (4+ 4X)x1+(4+8A)x2+(8+4X)x3
Subject to 1+3x2-x3 < 10
-x1+x2+2x3 < 15
2.01+x2+x3 < 20
X; > 0, i = 1,2, 3.
An optimal simplex tableau of the LP for = 0 is given below.
X2
X3 X4
X6
RHS
BV
0 17/5 0
3/3
1/5
0 8/5 0
3/5 -1/5
2/5 1/5
0 -1/5 2/5
0 2/5 16/5
1
15
X4
1
10
1
100 + OBJ
(a) Compute the characteristic interval for the optimal basis and identify the slope of
f(A), the optimal objective function value as a function of A, for A belongs to this
interval.
(b) Compute the new optimal solution if the RHS vector is replaced by (10, 20, 30)7
and A= 0

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