Calculator Input
Enter sensitivity report values and test the effect of a resource change.
Example Data Table
| Resource | Current Objective | Current RHS | New RHS | Shadow Price | Allowable Range | Estimated Objective |
|---|---|---|---|---|---|---|
| Labor Hours | 125,000 USD | 1,000 hours | 1,080 hours | 35 USD/hour | 920 to 1,120 | 127,800 USD |
| Machine Time | 86,500 USD | 500 hours | 470 hours | 18 USD/hour | 450 to 560 | 85,960 USD |
| Warehouse Space | 42,000 USD | 300 m² | 330 m² | 0 USD/m² | 260 to 380 | 42,000 USD |
Formula Used
Estimated objective change = Shadow Price × (Proposed RHS − Current RHS)
Estimated new objective = Current Objective + Estimated Objective Change
Valid RHS range = [Current RHS − Allowable Decrease, Current RHS + Allowable Increase]
The estimate is strongest when the proposed RHS stays inside the allowable sensitivity range. Outside that range, the optimal basis may change and the shadow price may no longer remain constant.
How to Use This Calculator
- Enter the resource or constraint name from your linear programming model.
- Type the current optimal objective value from your solved model.
- Enter the current RHS, proposed RHS, and the shadow price.
- Add the allowable increase and allowable decrease from your sensitivity report.
- Choose whether the constraint is binding or nonbinding and enter slack.
- Press the calculation button to view the estimated change above the form.
- Use the CSV or PDF buttons to save the result summary.
Frequently Asked Questions
1. What is a shadow price?
A shadow price is the marginal change in the objective value caused by increasing one constraint limit by one unit, while the current optimal basis remains unchanged.
2. When is the result reliable?
The result is most reliable when your proposed RHS stays inside the allowable increase and allowable decrease range reported by sensitivity analysis.
3. Why can a nonbinding constraint have zero value?
A nonbinding constraint already has slack. Adding more capacity usually does not improve the objective immediately, so its local marginal value is often zero.
4. Can the shadow price be negative?
Yes. A negative value means increasing the RHS would worsen the objective locally. This can happen in minimization settings or special model structures.
5. Does this replace solving the full model again?
No. It provides a fast sensitivity estimate. Large RHS changes can alter the optimal basis, so a full re-solve is better for exact decisions.
6. What do allowable increase and decrease mean?
They show how far the RHS can move up or down before the current basis may change. Inside that interval, the shadow price usually stays valid.
7. Why does this tool ask for slack?
Slack helps interpret whether the constraint is binding. Positive slack often indicates unused capacity and explains why the marginal value may be zero.
8. Can I use this for profit and cost models?
Yes. The calculator works for maximization and minimization models as long as you enter the shadow price and sensitivity limits from a valid solved model.