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Some inequality question

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From the information you've provided, you can conclude that any feasible solution has z≥1.

Let u = x1+x2+2x3

=> z = x1+u

x1≥0, u≥1 => z≥1

The constraint x1+x2+2x3≥1 limits how negative x2 can be for any combination of x1 and x3.

None of that tells you the optimal value, though. For that, you need to know the other constraints, and whether you're minimising or maximising.

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