Consider the following optimization problem Minimize z = x1 + 3x2 subject to 3x1 − 2x2 ≤ b1 x1 + 3x2 = 2 x1, x2 ≥ 0 (a) Solve the linear program graphically for b1 = 2. (b) By adjusting b1, determine graphically the range of b1 for which the solution stays optimal. (c) What is the range of the objective value for the range of b1 in Part(b)?
Consider the following optimization problem Minimize z = x1 + 3x2 subject to 3x1 − 2x2 ≤ b1 x1 + 3x2 = 2 x1, x2 ≥ 0 (a) Solve the linear program graphically for b1 = 2. (b) By adjusting b1, determine graphically the range of b1 for which the solution stays optimal. (c) What is the range of the objective value for the range of b1 in Part(b)?
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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Consider the following optimization problem
Minimize
z = x1 + 3x2
subject to
3x1 − 2x2 ≤ b1
x1 + 3x2 = 2
x1, x2 ≥ 0
(a) Solve the linear program graphically for b1 = 2.
(b) By adjusting b1, determine graphically the range of b1 for which the solution
stays optimal.
(c) What is the range of the objective value for the range of b1 in Part(b)?
(d) Deduce the relationship between the change in b1 to the change in objective
value?
(e) By adjusting b1, determine graphically the range of b1 for which the solution
stays feasible.
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