D 3.2-6. Suppose that the following constraints have been pro vided for a linear programming model. -x₁ + 3x₂ 30 -3x₁ + x₂ 30 and x₁ ≥ 0, x₂ = 0. (a) Demonstrate that the feasible region is unbounded. (b) If the objective is to maximize Z = -x₁ + x₂, does the mode have an optimal solution? If so, find it. If not, explain why no (c) Repeat part (b) when the objective is to maximize Z = x₁ - x (d) For objective functions where this model has no optimal solu tion, does this mean that there are no good solutions accord ing to the model? Explain. What probably went wrong whe formulating the model?

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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D 3.2-6. Suppose that the following constraints have been pro-
vided for a linear programming model.
-X₁ + 3x₂ 30
-3x₁ + x₂ 30
and
x₁ ≥ 0, x₂ = 0.
(a) Demonstrate that the feasible region is unbounded.
(b) If the objective is to maximize Z = x₁ + x₂, does the model
have an optimal solution? If so, find it. If not, explain why not.
(c) Repeat part (b) when the objective is to maximize Z = x1 - x₂.
(d) For objective functions where this model has no optimal solu-
tion, does this mean that there are no good solutions accord-
ing to the model? Explain. What probably went wrong when
formulating the model?
Transcribed Image Text:D 3.2-6. Suppose that the following constraints have been pro- vided for a linear programming model. -X₁ + 3x₂ 30 -3x₁ + x₂ 30 and x₁ ≥ 0, x₂ = 0. (a) Demonstrate that the feasible region is unbounded. (b) If the objective is to maximize Z = x₁ + x₂, does the model have an optimal solution? If so, find it. If not, explain why not. (c) Repeat part (b) when the objective is to maximize Z = x1 - x₂. (d) For objective functions where this model has no optimal solu- tion, does this mean that there are no good solutions accord- ing to the model? Explain. What probably went wrong when formulating the model?
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