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Aug 10, 2022 08:11 AM

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## What sorta questions are we answering from the sensitivity report?

- Amounts by which objective function coefficients can change without changing the optimal solution.

- The impact on the optimal objective function value of changes in constrained resources.

- The impact on the optimal objective function value of forced changes in decision variables.

- The impact changes in constraint coefficients will have on the optimal solution.

## Excel notation (Answer report) — optimal solution, final value of decision variables, resource usage

Section 1 and 2 together tell us the optimal values for the decision variables and the optimal value of the objective function (e.g. profit or return).

Section 3 gives info. on the constraints:

- Resource constraints:

- Which are binding i.e. which resources are all used up

- Which are non-binding i.e. some of the resource is not used

- Non-negativity constraints

- Which decision variables have values greater than their lower bound of zero

## Excel notation (Sensitivity report) — 1) Adjustable cells – final value, reduced cost, allowable increase/decrease; 2) Constraints – final value, shadow price, allowable increase/decrease;

## Variable section

## Further explanation of Reduced Costs

Def.:

- Products whose marginal profits are less than the marginal value of the goods required for their production will not be produced in an optimal solution (unless a constraint forces the product to be produced)

- Reduced costs tell us by how much we would have to increase the profitability of an item before it would be included in the optimal solution (for a maximisation problem). And vice-versa for a minimisation problem.

## Constraint section

## Why is the shadow price always 0 when `constraint = Non-binding`

?

(because adding more of resource that has not been used up is no help!

## Degenerate

### The 100% Rule determines if the current solution remains optimal, when more than one objective function coefficient changes.

**Problem**

**:**But what if I wanna examine the if the current solution remains optimal WHEN there is more than one objective function coefficient changes?

**Solution**: Then we need The 100% rule.

#### Two situations could arise when applying this rule:

- Case 1. All variables whose objective function coefficients change have nonzero reduced costs. (全部RC 唔係0)

#### How to perform:

## Excel notation (Limits report) — how the objective function varies as each variable ranges between its limits;

## To be studied further:

10 M + 15O + 10T ≤ 60

**Author:**Jason Siu**URL:**https://jason-siu.com/article/658d6d6c-86cf-4767-bbeb-b03d3d6612d5**Copyright:**All articles in this blog, except for special statements, adopt BY-NC-SA agreement. Please indicate the source!

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