A limiting factor is any scarce resource that limits how much an organization can produce. To maximize profits given a limiting factor, the contribution per unit of the limiting factor should be calculated for each product and the products ranked in this order. The scarce resource is allocated to production in this ranking until it is fully utilized to determine the optimal production plan. In the example, material is the limiting factor. Calculating contribution per kg of material ranks Product 3 first, so it is produced to its maximum demand. Remaining material is allocated down the ranking until used up, maximizing contribution and profit.

1. Limiting factor/key factor
(existence of shortage)
A limiting factor or key factor is 'anything which limits the activity
of an entity. An entity seeks to optimise the benefit it obtains
from the limiting factor. Examples are a shortage of supply of a
resource or a restriction on sales demand at a particular price'. -
CIMA Official Terminology
A limiting factor is any factor which is in scarce supply and which
stops the organisation from expanding its activities further, that
is, it limits the organisation’s activities. Example machine
capacity, skilled labour, material

2. Limiting factor
Contribution per unit of limiting factor (scarce resource) is
used
In a limiting factor situation, contribution will be maximised
by earning the biggest possible contribution per unit of
limiting factor (scarce resource).
The contribution per limiting factor should be maximised as
this will in turn maximise the contribution and hence the
profit of the business as a whole

3. Limiting factor
Points to bear in mind –
Fixed costs will remain the same irrespective of the
production plan
Units of output are divisible and optimal output may
include fractions of units
Limiting factor analysis is a method used for decision
making in the short term with one limiting factor. If there
are two or more scarce resources, then linear
programming should be used instead.
One qualitative factor may be the loss of customer
goodwill due to the company being unable to supply all of
its regular customers.

4. Limiting factor
The usual objective in questions is to maximise profit. Fixed costs
unchanged in the short run hence contribution maximised
Step 1: identify the scarce resource.
Step 2: calculate the contribution per unit for each product.
Step 3: calculate the contribution per unit of the scarce resource
for each product.
Step 4: rank the products in order of the contribution per unit of
the scarce resource.(highest = 1st)
Step 5: allocate resources using this ranking until scarce resource
is used up (optimal production plan)

5. Limiting factor- example
Data relates to a company manufacturing four products:
PRODUCT 1 2 3 4
Maximum demand (units) 1,000 1,550 1,250 1,375
£ £ £ £
Sales 30 54 20 25
VARIABLE COSTS:
Material 10 20 6 8
Labour 12 24 5 12
Contribution 8 10 9 5
The same material used for the production of all 4 products is in short supply and costs
£2/kg. Only 21,750kg available for the period in question.
Fixed costs = £12,000 for this period. Determine the optimal production plan to maximise
profits

6. Limiting factor– example solution
All 4 products have positive contribution
We need 29,750 kg (5x1000+10x1,550+3x1,250+4x1,375)
But material limited to 21,750kg
Therefore contribution per kg of material (limiting factor) for each product –
Ranking –
1st – Product 3
2nd – Product 1
3rd – Product 4
4th – Product 2
PRODUCT 1 2 3 4
Contribution 8 10 9 5
Material needed (kg) 5 10 3 4
Contribution per kg of material 1.6 (8/5) 1 (10/10) 3 (9/3) 1.25 (5/4)

7. Limiting factor– example solution
Allocating the scarce resource (material) using the ranking
Material limited to 21,750 kg
Optimal Production Plan of material consumption
Left
Product 3 – 1250 units x 3kg = 3,750 kg 18,000
Product 1 – 1000 units x 5kg = 5,000 kg 13,000
Product 4 – 1375 units x 4 kg = 5,500 kg 7,500
Product 2 – 750 units x 10 kg =7,500 kg -
21,750 kg

8. Limiting factor– example solution
PRODUCT 1 2 3 4 TOTAL
Production plan (units) 1,000 750 1,250 1,375
£ £ £ £ £
Contribution per unit 8 10 9 5
Contribution 8,000 7,500 11,250 6,875 33,625
Fixed costs (12,000)
PROFIT 21,625
Product 3 – 1250 units x 3kg = 3,750 kg
Product 1 – 1000 units x 5kg = 5,000 kg
Product 4 – 1375 units x 4 kg = 5,500 kg
Product 2 – 750 units x 10 kg =7,500 kg
21,750 kg
PROFIT generated using contribution per limiting factor -

9. Limiting factor– example solution
Production plan and Profit using ranking of contribution only rather than
contribution per limiting factor
Production plan
Product 2 – 1550 units x 10kg =15,500 kg
Product 3 – 1250 units x 3kg = 3,750 kg
Product 1 –
Product 4 –
500 units x 5 kg = 2,500 kg
0 units x 4 kg = 0 kg
21,750 kg
PRODUCT 1 2 3 4
Contribution (£) 8 10 9 5
PRODUCT 1 2 3 4 TOTAL
Production plan (units) 500 1,550 1,250 0
£ £ £ £ £
Contribution 4,000 15,500 11,250 - 30,750
Fixed costs (12,000)
PROFIT 18,750