ACCA Performance Management (F5) Certification Practice Exam

Which resource has a shadow price?

1. Any resource within the feasibility limit

2. The one that lies outside the feasible region

3. The resource that meets at the optimal point

4. All resources have a shadow price

The correct answer is: The resource that meets at the optimal point

In the context of linear programming and resource allocation, the shadow price refers to the value of an additional unit of a resource, particularly at the optimal solution point. This concept is crucial in understanding how resource constraints impact the objective function. When a resource meets at the optimal point, it signifies that this resource is a binding constraint. A binding constraint is one that, if relaxed, would allow an improvement in the objective function (such as increased profit or reduced costs). The shadow price for such a resource indicates how much the objective function would improve if there were an increase in the availability of that resource by one unit. Therefore, only resources that are part of the optimal constraint set can have a defined shadow price, indicating their economic value in the context of maximizing or minimizing the objective. Resources within the feasible limit may not necessarily affect the optimal decision, as they can be plentiful, and thus do not have a shadow price associated with them. Resources outside the feasible region suggest that they are not attainable given the current resource constraints, and thus, they cannot have a shadow price as they do not impact the current solution. While it might seem logical to consider all resources potentially having shadow prices, it's crucial to recognize that only those resources actively constraining the optimal point will