Page 98 - P1 Integrated Workbook STUDENT 2018

Chapter 6

Slack, surpluses and the shadow price

2.1 Slack and surpluses

Slack The amount of each resource which will be unused if a specific
linear programming solution is implemented.

Surplus This is utilisation of a resource over and above a minimum.
Surpluses tend to arise in minimisation of cost problems.

At the optimal production point, there will be no slack in the constraints whose lines
make up the optimal point. These are known as binding constraints.

2.2 The shadow price

Shadow price is the increase in contribution that could be created by having one
more unit of the limiting factor at the original cost. It is the opportunity cost of not
having the unit available.

To find the shadow price of a constraint:

 restate the relevant constraint, adding one more unit of the scarce resource

 find the new optimum solution

 the difference between the new contribution and the old contribution is the
shadow price of the constraint.

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