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Given the Following All-Integer Linear Programming Problem

question 14

Essay

Given the following all-integer linear programming problem:

Max 3x1 + 10x2

s.t.2x1 + x2 < 5
x1 + 6x2 < 9
x1 - x2 > 2
x1,x2 > 0 and integer

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?


Definitions:

Limbic System

A complex system of nerves and networks in the brain, involved with instinct and mood control, and the basic emotional drives.

Umami

One of the five basic tastes, characterized by a savory or meaty flavor, and attributed to the presence of glutamates and nucleotides.

Primary Tastes

The fundamental groups of tastes recognized by human taste perception, including sweet, sour, salty, bitter, and umami.

Sweet

A taste sensation often caused by the presence of sugars, perceived as pleasant and liked by most humans.

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