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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?


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