Given the Following All-Integer Linear Programming Problem

question 14

Essay

Given the following all-integer linear programming problem:
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Max 3x₁ + 10x₂
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s.t.2x₁ + x₂ < 5
x₁ + 6x₂ < 9
x₁ - x₂ > 2
x₁,x₂ > 0 and integer
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a.Solve the problem graphically as a linear program.
b.Show that there is only one integer point and that it is optimal.
c.Suppose the third constraint was changed to x₁ - x₂ > 2.1.What is the new optimal solution to the LP? To the ILP?

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Definitions:

Pleasure Principle

A concept in psychoanalytic theory referring to the instinctive drive to seek pleasure and avoid pain.

Reality Principle

A psychoanalytic concept where the ego seeks to satisfy the id's desires in realistic and socially appropriate ways.

Morality Principle

The concept that individuals have an inherent understanding of right and wrong that guides their behavior.

Conscience Principle

The ethical guideline that one's actions should be guided by conscience, reflecting an internal sense of right and wrong.