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13 Cards in this Set
- Front
- Back
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If increasing RHS increases Z, the shadow price will be |
Positive |
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If increasing RHS decreases Z, the shadow price will be |
Negative |
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If Z doesn't change, the shadow price is |
Zero |
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What causes SP = 0 |
Non binding constraint |
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Maximization Problem: Increasing the RHS of a ≤ constraint (expands, contracts) the feasible space, (increasing, decreasing) the value of Z, and generates a (positive, negative) SP. |
Expands Increasing Positive |
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Maximization Problem: Increasing the RHS of a ≥ constraint (expands, contracts) the feasible space, (increasing, decreasing) the value of Z, and generates a (positive, negative) SP. |
Contracts Decreasing Negative |
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Minimization Problem: Increasing the RHS of a ≤ constraint (expands, contracts) the feasible space, (increasing, decreasing) the value of Z, and generates a (positive, negative) SP. |
Contracts Decreasing Negative |
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Minimization Problem: Increasing the RHS of a ≥ constraint (expands, contracts) the feasible space, (increasing, decreasing) the value of Z, and generates a (positive, negative) SP. |
Expands Increasing Positive |
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Shadow Price Formula |
(new z - old z) / (new RHS - old RHS) |
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Shadow Price: Definition |
Marginal valuation The cost of producing using one more unit input Producer's opportunity cost of the next unit Either increase price (use input) or discount price (don't meet requirements) |
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SP Mathematical Rule |
Slack * SP = 0 |
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Slack |
RHS - LHS |
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Shadow Price Interpretation |
* Within the range of allowable decrease thru allowable decrease, optimal activity levels stay the same, but objective value changes by shadow price if we increase or decrease RHS by 1 |
