This document discusses limiting factor analysis for multi-product decision making. It provides steps to determine the optimal production plan using the limiting factor to maximize contribution or profit. The steps include determining the limiting factor, calculating contribution per unit of the limiting factor, ranking products based on contribution per unit of the limiting factor, and using the limiting factor to produce products in the ranked order. An example is provided to illustrate the solution.

1. Limiting
Factor
Decision
Presenter: Amzad Hossain

2. 2
Basic
Where there is a factor of production that is limited in
some way by:
• Scarce raw materials.
• Shortage of skilled labour.
• Limited machine capacity.
• Finance (see capital rationing in FM).
Aim: Maximize the contribution per unit of limiting factor

3. Limiting factor analysis
Determine
optimum
Yes production
using
contribution /
Is there just
limiting factor
one
constraint?
Determine
optimum
No production
using linear
programming
Slide 3

4. Examined 6/10
Key terms
Slack – maximum availability of a resource
has not been used.
Surplus – more output has been made than
the minimum requirement.
Slide 4

5. Key term
Shadow price
The additional contribution from having
1 more unit of scarce resource
This is the maximum extra you would
pay for 1 more unit
Slide 5

6. 6
Steps for problem solution
• Contribution per unit of sale.
• Contribution per unit of scarce resource.
• Rank in order of 2 - highest first.
• Use up the resource in order of the ranking.

7. Examined
Graphical linear programming 6/08
Formulate the model
a) Define variables
b) Formulate objective function
c) Formulate constraints
Solve the Problem
d) Plot constraints on a graph
e) Identify feasible space
f) Plot slope of objective function and slide to optimal point
g) Calculate value of objective function
Slide 7

8. 8
Assumption

9. 9
Example: Neal Ltd - Q
Neal Ltd produces two products using the same machinery. The hours
available on this machine are limited to 5000. Information regarding the
two products is
detailed below:
Products (per unit data) M N
Selling price (£) 40 30
Variable cost (£) 16 15
Fixed cost (£) 10 8
Profit (£) 14 7
Machine hours 8 3
Bud. sales (units) 600 500
Required: Calculate the maximum profit that may be earned.

10. 10
Example: Neal Ltd - Q
Using the previous example, Neal Ltd is now able to buy in the
products at the following costs:
Products (per unit data) M N
Purchase price(£) 24 21
Required: What is the revised production schedule and the
maximum profit earned?

11. 11
Example: Neal Ltd solution
Step 1: Calculate the extent of Limiting factor (shortage)
Product M 600 units x 8 hours/unit = 4,800 hours
Product N 500 units x 3 hours/unit = 1,500 hours
Total hours required = 6,300 hours
Hours available = 5,000 hours
Shortage = 1,300 hours
i.e. hours at present are not sufficient to fulfill demand for
both products so we will have to develop the optimal
production plan using 5,000 hours which maximizes the
profit.

12. 12
Example: Neal Ltd solution
Step 2: Calculate contribution per unit M N
24 15
Step 3: Calculate contribution per hour 3/hour 5/hour
Ranking 2 1
Step 4:
Develop optimal (most profitable) production plan using 5,000 hours
Product 1 (N) 500 units x 3 hours per unit = 1,500 hours
Leaving 3,500 remaining hours to be allocated to product 2 (M)
3,500 hours / 8 per unit = 437 units

13. 13
Example: Neal Ltd solution
Step 5: Total contribution from M and N
M (437 unit x 24 per unit) 10,488
N (500 units x 15 per unit) 7,500
Total contribution 17,988
Less: fixed cost 10,000*
Total profit 7,988
*Fixed cost (M =10 x 600 + N = 8 x 500)

14. 14
Example Neal Ltd solution
M N
Variable cost to make 16 15
External purchase price 24 21
Make Make
Based on the above comparison both products should be made
internally, but due to limited plant capacity only 437 units can be
produced as per 6 (a), therefore in order to fulfill the demand of
M, remaining 163 units will have to be bought in.

15. 15
Example Neal Ltd solution
Revised Contribution
M on first 437 units x 24 per unit = 10,488
on the purchased units (163 units x 16 per unit) = 2,608
N (as per previous working) = 7,500
Total contribution 20,596
Less: fixed cost 10,000
Revised Profit 10,596

16. 16
Example
XYZ company makes two products, standard
and deluxe. Relevant data are as follows:
Availability
Standard Deluxe per month
Profit per unit $15 $20
Labour hours per unit 5 10 4,000
Kgs of material per unit 10 5 4,250

17. 17
Solution

18. 18
Solution cont…

19. 19
Solution cont…

20. Cost volume profit
(CVP) analysis

21. Basic CVP analysis
You will have already encountered CVP
(or breakeven) analysis in your earlier
studies.
The F5 syllabus sees calculations such
as the C/S ratio and margin of safety
applied to multi-product situations.
Slide 21

22. 22
The C/S ratio

23. 23
The Margin of Safety

24. 24
Break-even analysis

25. Multi-product breakeven
Remember! To carry out this analysis, a constant product
sales mix must be assumed.
STEPS – Calculating breakeven point for multiple products
1) Calculate the contribution per unit
2) Calculate the contribution per mix
3) Calculate the breakeven point in number of mixes
4) Calculate the breakeven point in units and revenue
Slide 25

26. 26
Example
J Co produces and sells two products M & N.
The M sells for $7 per unit and has a
Total variable cost of $3 per unit.
The N sells for $15 per unit and has a total variable
cost of $5 per unit.
For every five units of M sold, one unit of N
will be sold.
Fixed costs total $30,000.
Calculate breakeven revenue?

27. 27
Example

28. Example
IB Co. makes two products, the Y and the Z. Details for
one unit of each are:
Y Z
Sales price ($) 10 12
Variable cost ($) 6 9
For every two units of Y sold, three units of Z will be sold.
Fixed costs are $340,000
What is the breakeven point?
Slide 28

29. Example cont…..
1) Calculate the contribution per unit
2) Calculate the contribution per mix
3) Calculate the breakeven point in number of mixes
4) Calculate the breakeven point in units and revenue
1. Y = $4, Z = $3
2. ($4 x 2) + ($3 x 3) = $17
3. Fixed costs/Cont. per mix = $340,000/$17
= 20,000 mixes
4. Y = 20,000 x 2 units
= 40,000 units ($400,000 in revenue)
Z = 20,000 x 3 units
= 60,00029
Slide
units ($720,000 in revenue)

30. Contribution to sales (C/S) ratio –
multiple products
Breakeven point in terms of sales revenue:
Fixed costs / average C/S ratio
STEPS – Breakeven using C/S ratio
1)Calculate the revenue per mix
2)Calculate the contribution per mix
3)Calculate the average C/S ratio
4)Calculate the total breakeven point
5)Calculate the revenue ratio of mix
6)Calculate the breakeven sales
Slide 30

31. Calculation of breakeven using C/S ratio
Using the earlier IB Co. example:
1. Selling prices - Y = $10, Z = $12
Revenue per mix = ($10 x 2) + ($12 x 3) = $56
2. Contribution per mix (see calc in last e.g.) = $17
3. Average C/S ratio = $17/$56 x 100% = 30.35714%
4. Total breakeven revenue = Fixed costs / C/S ratio =
$340,000 / 0.3035714 = $1,120,000 (nearest $1)
5. Revenue ratio per mix = ($10 x 2):($12 x 3) = 20:36 = 5:9
6. Breakeven sales: Y = $1,120,000 x 5/14 = $400,000
Z = $1,120,000 x 9/14 = $720,000
Slide 31

32. Target profits – multiple products
Approach 1 Approach 2
1) Calculate the contribution per 1) Calculate the average C/S
mix ratio
2) Calculate the required 2) Calculate the required total
number of mixes revenue.
3) Calculate the required
number of units and sales
revenue of each product.
Contribution to achieve a target profit (p) is fixed
costs plus p.
Slide 32

33. Calculating margin of safety
Steps:
• Calculate the breakeven point in
revenue
• Calculate the margin of safety
Example:
Budgeted sales are $70,000 and breakeven sales are $60,000.
Margin of safety = Budgeted sales – Breakeven sales
Margin of safety = $70,000 – $60,000
Margin of safety = $10,000 (or 14% of budgeted sales).
Slide 33

34. Breakeven chart
Assumption: Sales proportions are fixed
Revenue
$
Total costs
Breakeven
point
Variable costs
Margin of Fixed costs
safety
units
Slide 34

35. Multi-product P/V chart
Example of a P/V chart
6 Breakeven
point
Profit
0
$’000 14 41 50 65
12 Revenue$
Fixed costs
’000
Product 1
Product 2
20 Product 3
Slide 35

36. P/V charts - analysis
P/V chart - What does it
highlight? Sensitivity analysis
Overall company breakeven How will a result alter if estimates
point of variable values or
assumptions change?
Which products should be
expanded/discontinued Highlights risks an existing cost
structure poses.
The effect of changes in selling
price and sales revenue on Variable cost/price changes –
breakeven and profit. alter the slope of the P/V graph.
Average profit earned from sales Fixed costs change point of
of products in the mix intersection, but do not alter the
slope.
Slide 36

37. 37
Limitations/Assumptions of CVP
• Costs behaviour is assumed to be linear
• Revenue is assumed to be linear
• Volume Produced = Volume Sold
• Ignores inflation
• Assumes a constant sales mix