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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