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If the right-hand side of a constraint changes beyond its allowable range, does the shadow price just stay the same or change?

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The current shadow price becomes invalid. Beyond the range of feasibility, the optimal basis changes, meaning a new corner point becomes optimal with a different shadow price.

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If the right-hand side changes past its allowable range, the shadow price will change. This happens because a different resource becomes the new bottleneck, meaning the old shadow price is no longer accurate.

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