45205333 ACCA F2 Management Accounting Course Slides

ACCA Paper F2 – Management accounting

Course slides

Syllabus A

The nature and purpose of cost and management accounting

B

Cost classification, behaviour and purpose

C

Business mathematics and computer

D

spreadsheets Cost accounting techniques

E

Budgeting and standard costing

F

Short-term decision-making techniques

Slide 6

Format of the Exam

Format of the Exam 1 mark question

Marks

10 questions

10

Paper based exam: All multiple choice with a choice of 2 or 3 answers. Predominantly „wordy‟ questions.

2 mark questions

Total Slide 7

40 questions

80

Paper based exam: All multiple choice with a choice of 4 answers including words and calculations. 90

The BPP Learning Media classroom slides What do these slides cover? – A selection of key areas of the syllabus

Using the slides – Use the slides as a point of reference – Add detail by talking around the slides (eg using material from the corresponding Study Text chapter) – Consider adding slides yourself to suit your course – Recommend students attempt appropriate questions from the Practice & Revision Kit

Slide 8

Chapter 1

Study Text Chapter 1

Information for management

Purpose

• Assist management in running their business to achieve an overall objective • What is the overall objective of a business?

Slide 10

Data and information

• Data is the RAW MATERIAL

• Information is the PROCESSED DATA

Slide 11

Planning, control and decision making • Planning – Long term strategies – Short term targets • Control – Performance of the organisation – Review corporate plan • Decision making – autonomy of managers

Slide 12

Key roles of a management accountant • Costing • How to put a cost on our products and services

• Decision-making • What to produce/how should we finance it etc • Assessment of business requirements/budgeting • Planning

• Control • Assessing inefficiencies

• Performance Evaluation • Comparison to targets

Slide 13

Chapter 2


Cost classification

Introduction • Arrange costs into logical groups – By function e.g. production, admin, finance – By nature e.g. labour, materials, stationery

• Grouping by function: Pool of costs

Production costs

Slide 15

Non production costs

Introduction • Grouping by nature: Pool of costs

materials

Slide 16

Labour

Expenses

Cost classification £ Productioncosts

Non-production costs TOTAL COST/EXPENSES

Slide 17

X

X X

Direct Prod‟n cost Indirect Prod‟n cost

Admin costs Selling & Distribution

Cost classification Direct Production costs Directmaterials Direct labour Directexpenses Indirect Production costs Indirectmaterials Indirectlabour Indirectexpenses TotalProductioncosts Non-production costs Administrationcosts Selling and distribution costs TOTACLOSTS Slide 18

X X X X X X X X X X

A typical cost card for a cost unit Direct Production costs Direct materials (5kg @ $3/kg) Direct labour (3hrs @ $6/hr) PRIME COST Indirect Production costs Variableoverheads Fixedoverheads FULLPRODUCTCOST

Slide 19

15.00 18.00 33.00 2.00 3.00 38.00

Terminology • Cost object • Cost unit • Divisional structures – Cost centre – Profit centre – Revenue centre – Investment centre

Slide 20

Chapter 3


Cost behaviour

Accountant‟s Linear Assumption •Accountant‟s version •Economist‟s version

Y = a + bX

Total cost ($) Variable cost (VC)

Fixed cost (FC) output

Total cost = Fixed cost + (VC/unit x Output) Slide 22

„Hi-Low‟ Method Four step approach 1. Find the highest and the lowest output and the total costs at these levels of output. 2. Find the difference in output units and total cost. 3. Calculate the variable cost per unit (VC/unit). 4. Calculate the fixed cost by substitution.

Slide 23

Chapter 4


Correlation and regression; expected values

Costs vs output - scattergraph

$

y = a + bx

(y) dependent variable

(x)

output independent variable

Slide 25

Linear regression • Finds the mathematical line of best fit y = a + bx b= n xy- x y 2

2

n x - ( x) a=

y-b x n

Slide 26

n

Correlation coefficient r=

n xy- x y ([n (x2)- ( x) 2][n (y2)-(

y) 2])

-1 < r < +1

Slide 27

r = +1

- perfect positive correlation

r = -1

- perfect negative correlation

r=0

- no correlation

Coefficient of determination The amount of variation in y which appears to be explained by variation in x Does NOT prove “cause and effect” Coefficient of determination = r2

Slide 28

Expected Values • Long term weighted average of possible outcomes: • Expected Value (EV) = np – If +ve EV = accept – If -ve EV = reject

Slide 29

Chapter 5


Spreadsheets

Definition

• Electronic piece of paper • Divided into rows and columns • Data is input into „cells‟ i.e. A5, D8 • Data can either be numbers, text or symbols • Output is derived by applying a formula to data cells e.g. addition A5 + D8 Slide 31

Uses of spreadsheets • Preparation of management accounts • Cash flow analysis, budgeting and forecasting • Account reconciliation • Revenue and cost analysis • Comparisons and variance analysis • Sorting and categorisation of data Slide 32

Formulae with conditions • We can build a range of options into our data • = IF (logical_test, value_if_true, value_if_false) Example • = IF (A5>500,”Hurray!”,”More Sales Please!”)

Slide 33

Presentation of spreadsheets • Split into sections; Inputs, Calculations and Results • Use titles and column and row headings data source and purpose of • State spreadsheet

• Apply consistent format i.e. 2 decimal places • Use colours, borders and shadings to highlight and differentiate Slide 34

Chapter 6


Material costs

Order, receipt and issue of raw materials Purchase requisition

Purchase order

Goods received note

Slide 36

Accounting for materials Materials inventory account (1) Material purchased X

__ X

Slide 37

(2) Issues to production X

c/d closing inventory balance

X

__ X

Monitoring inventory levels • To maintain accurate records of inventory • Visual methods of inventory control • Theoretical methods of inventory control – Re-order level – Minimum level – Maximum level

Slide 38

Learn for the exam

Costs associated with stock

Purchase costs

PxD

+ Order costs

C x D/Q

+ Holding costs

H x Q/2

= TOTAL COSTS Slide 39

WANT TO MINIMISE THESE

Economic order quantity • Number of units to order to minimise costs

EOQ

2

CoD Ch

Given in Exam

Slide 40

Discounts • Available above a certain order quantity • Is it worth ordering above the EOQ to get the discount? • Steps: – Calculate EOQ – Recalculate EOQ if it falls within a discount band – Calculate total costs at EOQ – Calculate total costs at the lower boundary of each discount band Slide 41

Economic batch quantity • Used when stock replenished gradually – internally or; – from supplier

• Similar to EOQ but factors in replenishment rate • Total EBQ never held in stock – as stock is being replenished during the period

Slide 42

Economic batch quantity EBQ

2CoD

Ch 1

D R

Total holding costs in period

Total set up costs in period

Slide 43

Given in Exam

Q 1 2

D Q

D Ch R

Co

Chapter 7


Labour costs

Method of remuneration • Time-based systems

• Piecework systems

• Bonus/incentive schemes Slide 45

Measuring labour activity • Productivity • Standard hours of production • Efficiency x capacity = production volume

Slide 46

Accounting for labour costs • Direct or Indirect labour – learn the rules • Ledger accounting – Dr Wages account Gross wages – Cr Bank / PAYE / NIC accounts

Slide 47

– Dr WIP account – Cr Wages account

Direct wages Direct wages

– Dr Production o/h – Cr Wages account

Indirect wages Indirect wages

Labour turnover • The rate at which employees leave the company • Reasons may be controllable or uncontrollable by the company

Slide 48

Chapter 8


Overheads and absorption costing

Cost card •

Aim

–

to find the full cost of one unit

$/unit Direct materials 4kg @ $2/kg Direct labour 3 hrs @ $7/hr Primceost

X X

Overheads FullProductcost

Slide 50

Allocate

X X X

3 Steps

Absorption costing method Total Production Costs Direct Costs

Indirect Costs (overheads)

1.Allocate & Apportion

COST CENTRES

Allocate

Production 1

Production 2

Service

Production 1

Production 2

2.Reapportion

3. Absorb

COST UNIT Slide 51

Overheads – step 1 Total Production Costs Direct Costs



COST CENTRES

Allocate

Production 1

COST UNITS Slide 52

Production 2

Service




COST CENTRES

Allocate

Production 1

Production 2

Service

Production 1

Production 2

2.Reapportion

COST UNITS Slide 53

Reapportionment To reapportion service cost centre overheads to production cost centres there are 2 methods Direct Method

Inter-service department work is ignored Slide 54

Reciprocal Method

All inter-service department work is recognised




COST CENTRES

Allocate

Production 1

Production 2

Service

Production 1

Production 2

2.Reapportion

3. Absorb

COST UNIT Slide 55

3. Absorb The final step is to charge these overheads to cost units. This is called absorption. Production overhead OAR (overhead absorption rate) =

_______________ Activity level

What activity level should you use?

Slide 56

3. Absorption bases (a)Perunit

OAR/unit

(b)Perlabourhr

OAR/labhr

(c) Per machine hr

OAR/mach hr

(d) % Direct Labour cost

OAR/$ labour

(e) % Direct material cost

OAR/$ mats

(f) % Prime cost Slide 57

OAR/$ prime cost

Pre-determined OARs Businesses estimate (or pre-determine) their OAR at the start of the year OAR =

Production Overhead __________________ Activity level

BECOMES….. Pre-determined OAR =

Budgeted overhead _________________ Budgeted activity level

Slide 58

Cont. Businesses want to record overheads regularly during the year

Overhead = Actual Activity (eg labour hrs) Absorbed

Slide 59

x

Pre-determined OAR

Cont. At the end of the year actual overheads will be known

Overhead Absorbed

Actual Overhead

Difference = under or over absorption

Slide 60

Reasons for under/over absorption Why do we get an under or over absorption? Budgeted overhead Pre-determined = _________________ OAR Budgeted activity level

Budgeted overhead Actual overhead Expenditure variance Slide 61

Budgeted activity Actual activity Volume variance

Non production overheads • For internal reporting non-production overheads can also be allocated to units • One approach may be:

OAR =

Non-Production Overhead Production overhead

Slide 62

X 100

Chapter 9


Marginal and absorption costing

Cost card – marginal costing $/unit

Slide 64

Directmaterials

X

Directlabour

X

Variable overhead Marginalcost

X X

Used to value stock under Marginal costing

Fixedoverheads

X

Full product cost

X

Used to value stock under Absorption costing

Contribution Contribution = selling price less ALL variable costs

$ Selling price Less: Variable production costs Variable non-production costs Contribution

Slide 65

X X X (X) X

Marginal costing profit statement

$ X

Sales Cost of sales

Opening Stock

(@ Marginal cost)

Production costs: Variable costs (mats, lab, var.overhead) Closing Stock

(@ Marginal cost)

X X (X) _____ (X)

Variable non production costs Contribution

(X) ____ X

Less: Fixed costs

(X) ____

P Nreotfit Slide 66

X

Absorption costing profit statement

$ X

Sales Cost of sales

Opening Stock

(@ Full cost)

Production costs: Variable costs (mats, lab, var.overhead) Fixedoverheadsabsorbed

X X X

Closing Stock (@ Full cost) (X) Overhead = Actual Activity X OAR Adjustment X/(X) Absorbed for under/(over) absorption _____ (X) ____ GroP srsofit X Non production costs (sales, distribution, admin) ____ X P Nreotfit Slide 67

X

Reconciliation proforma Year1 $

Absorption costing profit Add: Fixed overhead in opening stock Less: Fixed overhead in Closing stock = Marginal costing profit

Slide 68

Year2 $

Reconciling profits Difference in profit

= Change in stock

X

OAR/unit

But which profit is higher AC profit Or MC Profit? Production Closing stock AC Profit Slide 69

> = < > < = > < =

Sales Opening stock MC Profit

Chapter 10


Process Costing

Introductory example – a party • a barrel holds 100 pints of beer and costs $100 much we • How charge per should pint to cover our costs?

$100 = $1/pint 100 pints Slide 71

However…… Will you get the full 100 pints from your barrel?? We only actually expect to get 95 pints

Normal loss = 5 pints So… what should we charge now per pint?

$100 = $1.05/pint 95 pints Slide 72

Normal loss – eg barrel dregs! What could we do with our loss? A local gardener likes the dregs for his plants – he‟ll pay 20p per pint, we could use this to reduce our costs. So… what should we charge now per pint?

x 5value pints) - scrap $100 - (20¢ = $1.04/pint 95 pints Slide 73

Cont. So how have we found the cost of a pint to charge our party goers? Cost per unit = Input costs - Scrap value of normal loss ________________________________ Input units - Normal loss units

Learn this formula! Slide 74

But…… What about unexpected losses?? At the end of the party we realise that we didn‟t get the 95 pints we expected we only got 85.

Abnormal loss = 10 pints Its too late to charge more, we have already charged $1.04 per pint….… …its just our loss we‟ll have to cover the $1.04 for each pint we didn‟t sell Slide 75

Finally….good news What if losses weren‟t as much as we expected? At the end of the party we realise that instead of the 95 pints we were expecting we actually got 98 pints from the barrel.

Abnormal gain = 3 pints We expected to scrap them for 20¢ – we actually sold them for $1.04 Slide 76

Normal Loss • Normal loss = expected loss Good output Inputs

Slide 77

Process 1

Normal loss

Abnormal loss or gain • Abnormal loss = unexpected loss • Abnormal gain = unexpected gain

Good output Inputs

Process 1

Normal loss Abnormal loss / gain

Slide 78

Recap – Process costing 1

Units calculation

2

Set up the process account and complete as far as possible

3

Calculate cost per unit:

4

Valuations & transfer to process account

Slide 79

Input units = Good output + NL +/(-) AL/(AG)

CPU = Input cost - scrap proceeds from normal loss Input units – normal loss units

Introduction to WIP Input costs - Scrap value of normal loss ________________________________ Cost per unit = Input units - Normal loss units

BUT….What if units aren‟t finished? MAY HAVE…..

Slide 80

Introduction to WIP

Finished unit

WIP units

We can‟t give them the same value Slide 81

Equivalent units Output from process includes:

½unit

+

½unit

+

1 whole unit

2 equivalent whole unit cost per equivalent unit Slide 82

Previous processes

Process I

Process II

• Process 1 is another input • OWIP 100% complete for Process 1

Slide 83

Summary and question approach 1

Units calculation

2

Set up the process account and complete as

3

far as possible Complete statement of equivalent units

4

Calculate cost per equivalent unit

5

Valuations & transfer to process account

Slide 84

Opening WIP + Input = Good output + NL +/(-) AL/(AG) + Closing WIP

Chapter 11


Process costing, joint products and by-products

Joint products and by-products

Joint products

forestry By product Slide 86

Joint products and by-products Product 1

Inputs

Process (Joint costs)

Separation point

Slide 87

Product 2

By-product

Joint products and by-products - accounting

Joint products Substantial sales value

• Apportion joint costs – Various methods: as specified in question

Slide 88

By-products Relatively low sales value Secondary to process • Do not allocate costs – USUAL occurrence: reduce process costs – ONE-OFF: misc income

Chapter 12


Job, batch and service costing

Job and batch costing • Job = a cost unit of a single order/contract • Batch = a cost unit which consists of a separate, readily identifiable group of units

Slide 90

Job cost cards Job XYZ $ Direct materials

X

Direct labour (hrs @ $/hr) Variable overheads (hrs @ $/hr) Prim coest

X X X

Fixed overheads Tocto alst

X X

Profit Sellingpriceojfob

Slide 91

X X

Cost structures If profit is 20% of cost

If profit is 20% of sales price

Selling price

120%

Selling price

100%

Costs

100%

Costs

80%

Profit

20%

Profit

20%

MARK - UP Slide 92

MARGIN

What are service organisations? • Don‟t make or sell a tangible product • Profit making or not-for-profit sector Accountancy firms, hotels, schools, – E.g. hospitals

• Service costing v. other product costing – Cost of direct materials is small – Unit cost is difficult to calculate – Costing will vary from one service to another Slide 93

Cost per unit

Cost per unit =

Total costs for a period ______________________________ Number of service units in the period

But what is a service cost unit ?

Slide 94

Composite cost unit A composite cost unit takes into account several elements of a service e.g. excess baggage service Cost per KG? OR Cost per mile transported?

Cost per KG/mile Slide 95

Service department costing • Cost of an „internal service‟ • Purposes of service department costing – Control costs and efficiency – Prevent unnecessary use of services • What cost to charge to user dept – No charge – Total actual cost – Standard absorption cost – Variable cost – Opportunity cost – Cost plus a margin for profit Slide 96

Chapter 13


Budgeting

Planning and control • Planning and control cycle Determine objectives

Control - variances

Planning

Actual operations

Slide 98

–

set budget

Preparation of budgets • Budget period • Budget manual • Budget committee

Slide 99

Fixed and flexible budgets • Fixed budget = Master (srcinal) budget – Prepared at the start of the budget period

• Flexible budget = „scenario planning‟ – Prepared at the start of the year – What if? analysis – Flexed budget is a flexible budget prepared at the end of the year using the actual volumes

Slide 100

Chapter 14


Standard Costing

Standard Costing WHAT IS A STANDARD COST? • An estimated unit cost • For example: – Direct materials

3kg x $2/kg

$6

» Based on standard usage ie 3kg / unit » Based on standard cost / kg ie $2 / kg

Slide 102

Lecture example 1 • Ideal standard



perfect operating conditions

• Current standard



use last year

• Basic standard



leave unaltered over long period

• Expected standard



attainable improvements

Slide 103

Chapter 15


Basic variance analysis

Variances

actual results

DIFFERENCES =

expected results

VARIANCES

Can be FAVOURABLE Slide 105

Variances

actual results

DIFFERENCES =

expected results

VARIANCES

Or ADVERSE Slide 106

Cost variances Materials usage variance

Materials price variance

Unit cost Direct Materials

3kg x $2 / kg

$6

Direct Labour

4hrs x $6 / hr

$24

Labour efficiency variance

Labour rate variance

Variable overheads 4hrs x $2 / hr Var o/h efficiency variance

Marginal cost Slide 107

$8

Var o/h expenditure variance

$38

Basic cost variances • For example: materials price variance – Actual purchases SHOULD cost

x

• Actual purchases x standard cost

– Actual puchases DID cost • Actual purchases x actual cost

Slide 108

x x

Basic cost variances • For example: Materials usage variance – Actual production SHOULD use

x kg

• Units produced x standard usage

– ActualproductionDIDuse • Units produced x actual usage

• Value at standard cost / kg

Slide 109

xk g x kg $x

Fixed overhead variances Fixed overheads Total variance Expenditure variance

Volume variance Efficiency variance

Slide 110

Over/underabsorption

Capacity variance

Causes of variances • C ontrollable expenditure • A ccuracy – measurement of data • U ncontrollable expenditure • S tandard type • E xpectations – unrealistic standard

Slide 111

Interdependence of variances Variances may affect each other e.g. Cheaper materials Inferior quality

Slide 112

Favourable price variance Adverse usage variance (& labour efficiency?)

Interdependence of variances Variances may affect each other e.g. Increase in sales price Favourable price variance Fall in demand

Slide 113

Adverse sales volume variance

Chapter 16


Further variance analysis

Operating statement MC Budgetedcontribution Sales volume variance Flexed budgeted contribution Sales price variance Variable cost variances Actual contribution Budgeted fixed o/h Fixed o/h expenditure variance Actual fixed o/h Actuparlofit

Slide 115

x x/(x) x x/(x) x/(x) x

x x/(x) (x) x

Differences between MC and AC For Absorption Costing: • Sales volume variance – Difference between budgeted sales and actual sales units valued at standard PROFIT per unit under AC

• Fixed overhead variances – Calculate a fixed overhead volume variance. This can also be split into an efficiency and capacity variance

• Operating statement – Reconcile between budgeted profit and actual profit Slide 116

Operating statement AC Budgetep drofit

x

Sales volume variance Flexedbudgetedprofit

x/(x) x

Sales price variance

x/(x)

Cost variances (including fixed overheads

x/(x)

Actup arl ofit

Slide 117

x

Chapter 17


Cost-volume-profit Analysis

Introduction £ Sales Less:VCs

15,000 (5,000) _____

Contribution

10,000

Fixed ? costs

(10,000) ? _____ 0

Profit Slide 119

Must be EQUAL

Introduction So we will breakeven when… Contribution = Fixed costs Cont‟n/unit x Q = Fixed costs Fixed costs Q = __________ Cont‟n/unit

Slide 120

Breakeven Revenue – C/S Ratio In the last e.g. B/E Revenue = BEP x SP/unit Fixed costs x SP/unit B/E Revenue = __________ Cont‟n/unit B/E Revenue = Fixed costs x _________ Cont‟n/unit SP/unit _________ Cont‟n/unit SP/unit

Fixed costs __________ B/E Revenue C/S=ratio C/S ratio Slide 121

Margin of safety Margin of safety (in units) = Budgeted sales volume – breakeven sales volume

OR

Margin of safety (as %) = Budgeted sales volume – breakeven sales volume __________________________________________ X 100 Budgeted sales volume

Slide 122

Breakeven chart Total Revenue (TR)

TR = SP/unit x Q TR = $8/unit x Q if Q = 0, TR = 0 if Q = 5000, TR = 40,000 Slide 123

Breakeven chart Total Cost (TC)

TC = FC + VC/unit x Q TC = $5,700 + $6.50/unit x Q if Q = 0, TC = 5,700 if Q = 5000, TC = 38,200 Slide 124

Breakeven chart $ TR

40,000

Profit

TC

38,200 30,400

Fixed cost 3,800

5,000

Margin of safety Slide 125

Q

Profit volume chart Profit

$1,800

$0

3,800

5,000

Margin of safety ($5,700)

Slide 126

Q

Required profit level Fixed Fixed costscosts + required profit Sales volume to reach ______________________ ______________ Breakeven point = required profit level Contribution/unit

Slide 127

Chapter 18


Relevant costs and decision making

Relevant Costs • What is a relevant cost?

FUTURE

Only future costs are affected by our decision Slide 129

INCREMENTAL

i.e. incurred as a direct result of our decision

CASHFLOW

Only cash

Popular scenario with examiner

e.g. need 500kg of material for new project have 300kg in stock (cost $3/kg) current purchase price = $5/kg scrap value = $1/kg

what‟s the relevant cost of the 500kg? Slide 130

Relevant cost - materials Instock In continual use

No other use

Notinstock

Scarce

Just have to buy it Relevant

If take from stock will have to replace

If take from stock won’t have to replace

If take from stock can’t replace

Relevant cost = current purchase price

Relevant cost = scrap value foregone

Relevant cost = opportunity cost

Slide 131

cost = current purchase price

Relevant cost - labour labour Could hire more

Spare capacity

Full capacity

Relevant cost = current rate of pay

Relevant cost = nil

Relevant cost = opportunity cost

Slide 132

Relevant cost - labour Full capacity

E.g. labour is currently working on product A Product A Lose $ $ Sales revenue 50 Lose revenue 50 Materials (3) Save materials (3) Labour (1hr) Labour (1hr) (5) _____ _____ Contribution Loss to business 47 42 What do we lose if we take the labour away to work on a new product – B? Slide 133

Relevant cost

Relevant cost - labour Full capacity

E.g. labour is currently working on product A Alternative calc. Product A $ $ Sales revenue 50 Lost cont‟n 42 Materials (3) Add back labour 5 _____ Labour (1hr) (5) _____ Loss to business 47 Contribution 42 Relevant cost Slide 134

Deprival value • How to find the relevant cost of an asset Lower of..

Replacement cost

Higher of..

Net realisable value Slide 135

Value in use

Single limiting factor analysis 1

Identify limiting factor

2

Calculate contribution per unit

3

Calculate contribution per limiting factor

4

Rank products

5

Prepare a production plan

Slide 136

Chapter 19


Linear programming

Limited resources • A business needs to identify the optimal production plan for utilising its resources to maximise profit • 2 techniques – Single limiting factor – Linear programming (>1 limiting factor)

Slide 138

Example A business manufactures 2 products – garden gnomes and garden statues. Information for one unit of each product is given below: Gnome

Statue

Contribution

$6

$9

Material

2kg

4kg

Labour

5 hours

6 hours

There are only 80 kg of material available and 180 hours of labour. Demand for the statues will not be above 10 units per week.

Slide 139

Linear programming steps

1

Define variables

– let g = number of gnomes produced per week – let s = number of statues produced per week – let k = contribution per week

Slide 140

Linear programming steps 2

Establish constraints

– subject to: • Materials • Labour

2g+4s 80 5g + 6s 180

• Demand • Non-negativity

s 10 g,s > 0

3

Formulate objective function

– Max k = 6g + 9s

Slide 141


Plot constraints on graph

– Find co-ordinates • Materials

2g+4s=80 When g=0, s=20 s=0, g= 40

• Labour

5g+6s=180 When g=0, s= 30 s=0, g=36

• Demand • Non-negativity

Slide 142

s = 10 g,s > 0


s

Materials: 2g + 4s = 80

30

Labour: 5g + 6s = 180 Demand : s = 10

20

10

0 Slide 143

10

20

30

40

g


Identify feasible region

s

Materials: 2g + 4s

30

Labour: 5g + 6s Demand : s

80 180

10

20

10

B

C D

A 0 Slide 144

10

20

30

E

40

g


6

Plot objective function and identify optimal point

k = 6g + 9s Pick any value for k • Say k = 6 x 9 = 54 • k = 54 = 6g + 9s – When g=0, s=6 – When s=0, g=9

Slide 145


s

Materials: 2g + 4s

30

Labour: 5g + 6s Demand : s

80 180

10

k = 6g + 9s

20

Optimal point = D 10

B

C D

A 0 Slide 146

10

20

30

E

40

g


Solve using simultaneous equations

Materials Labour

2g + 4s = 80 5g + 6s = 180

(i) (ii)

Rearrange (i) to get g on own Materials

g = 40 – 2s

Substitute in (ii) Labour 5g + 6s = 180 (ii) 5(40 – 2s) + 6s = 180 200 – 10s + 6s = 180 200 – 180 = 4s Slide 147

s=5

Linear programming steps Substitute s = 5 in (i) Materials 2g + 4s = 80 (i) 2g + (4 x 5) = 80 2g = 80 – 20 g = 30 Optimal production plan: 30 Gnomes 5 Statues Contribution: k = 6g + 9s k = (6 x 30) + (9 x 5) = £225 Slide 148

45205333 ACCA F2 Management Accounting Course Slides

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