# B3: Decision Making Techniques | Limiting Factors (ACCA F5)

Limiting Factors looks at the limiting factors in scarce resource situations, determines the optimal production plan where an organization is restricted by a single limiting factor, explains how to formulate and solve multiple scarce resource problems, explains and calculates shadow prices and their implications and details how to calculate slack and highlights its importance in decision-making and performance management.

## Limiting Factors

A limiting factor is any scarce factor that prevents the organization from expanding its activities. A limiting factor results in a maximum capacity for companies because of the unavailability of the resource.

### a) Identify limiting factors in a scarce resource situation and select an appropriate technique.

Examples of limiting factors are labour, materials and machine capacity. An organization may be faced with one or more limiting factor. If there is one limiting factor, products are ranked by priority.

If there is more than one limiting factor, the following steps are taken:

1. Determine which resources are scarce
2. Rank the products in order of contribution per \$1 of direct materials consumed
3. Determine a production plan that takes the limits into consideration
4. Create a budget that maximizes profits

### b) Determine the optimal production plan where an organisation is restricted by a single limiting factor, including within the context of “make” or “buy” decisions.

For a detailed explanation of how to determine the optimal production plan, please refer to BPP’s ACCA F5 Performance Management Study Text.

### c) Formulate and solve multiple scarce resource problem both graphically and using simultaneous equations as appropriate.

Multiple scarce resource problems can be solved graphically using linear programming. The steps are:

1. Define the problem
• Define the variables
• Establish the constraints
• Construct objective function
2. Plot the constraints graphically
3. Establish the “feasible region for the optimal solution”
4. Determine what is the optimal solution

For examples, please refer to BPP’s ACCA F5 Performance Management Study Text.

Simultaneous equations are used after constraints have been determined graphically. The steps for using simultaneous equations are:

1. Define the variables
2. Establish the constraints
3. Construct the objective function (determine the contribution for each product)
4. Establish the feasibility region (on the graph)
5. Determine the optimal solution using simultaneous equations

### d) Explain and calculate shadow prices (dual prices) and discuss their implications on decision-making and performance management.

The shadow price is the “most extra” that the company is prepared to pay for “one extra unit of the limited resource.” It is calculated by “calculating the extra profit that would result” if there was one extra unit of the limited resource.

The shadow price is the “internal opportunity cost.” When there are limiting factors, there are opportunity costs. Priority is given to the product that results in the greatest incremental benefit.

For examples of how to calculate the shadow price, please refer to BPP’s ACCA F5 Performance Management Study Text.

### e) Calculate slack and explain the implications of the existence of slack for decision-making and performance management. (Excluding simplex and sensitivity to changes in objective functions)

Slack occurs when “maximum availability of a resource is not used. Surplus occurs when more than the minimum requirement of a resource is used.

Note: If the amount of resources used equals the amount of the resource available at the optimal solution, there is no spare capacity there is no slack.

Note: If the amount of resources used is less than the amount of the resource available at the optimal solution, there is spare capacity and there is slack.

For examples of how to calculate slack, please refer to BPP’s ACCA F5 Performance Management Study Text.