limiting factor 1

Limiting

Factor

Decision

Presenter: Amzad Hossain

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

Is there just

one

constraint?

Determine

optimum

production

using

contribution /

limiting factor

Determine

optimum

production

using linear

programming

Yes

No

Limiting factor analysis

Slack – maximum availability of a resource

has not been used.

Surplus – more output has been made than

the minimum requirement.

Examined 6/10 Key terms

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

Key term

6

• 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.

Steps for problem solution

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

Examined

6/08 Graphical linear programming

8

Assumption

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

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

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


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


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

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

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

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

Solution

18

Solution cont…

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Solution cont…

Cost volume profit

(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.

Basic CVP analysis

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The C/S ratio

23

The Margin of Safety

24

Break-even analysis

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

Multi-product breakeven

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?

26

Example

27

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?

Example

1) Calculate the contribution per unit


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

= 60,000 units ($720,000 in revenue)

Example cont…..

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

Contribution to sales (C/S) ratio –multiple products

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

Calculation of breakeven using C/S ratio

Approach 1

Approach 2


2) Calculate the required number of mixes

3) Calculate the required number of units and sales revenue of each product.

1) Calculate the average C/S ratio

2) Calculate the required total revenue.

Contribution to achieve a target profit (p) is fixed

costs plus p.

Target profits – multiple products

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).

Calculating margin of safety

Assumption: Sales proportions are fixed

units

$ Revenue

Total costs Breakeven

point

Variable costs

Margin of

safety Fixed costs

Breakeven chart

Example of a P/V chart

Revenue$

’000

Profit

$’000 0

20

12

6

14 41 65 50

Breakeven

point

Fixed costs

Product 1

Product 2

Product 3

Multi-product P/V chart

P/V chart - What does it

highlight?

Sensitivity analysis

Overall company breakeven point

Which products should be expanded/discontinued

The effect of changes in selling price and sales revenue on breakeven and profit.

Average profit earned from sales of products in the mix

How will a result alter if estimates of variable values or assumptions change?

Highlights risks an existing cost structure poses.

Variable cost/price changes – alter the slope of the P/V graph.

Fixed costs change point of intersection, but do not alter the slope.

P/V charts - analysis

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

limiting factor 1

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