f5 interim

Interim Assessment

KAPLAN PUBLISHING of 10

ACCA INTERIM ASSESSMENT

Performance Management

QUESTION PAPER Time allowed Reading time: 15 minutes Writing time: 3 hours Answer all questions Do not open this paper until instructed by the supervisor This question paper must not be removed from the examination hall

DECEMBER 2009

Kaplan Publishing/Kaplan Financial

ACCA F5 Performance Management

of 10 KAPLAN PUBLISHING

© Kaplan Financial Limited, 2009 All rights reserved. No part of this examination may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without prior permission from Kaplan Publishing.

Interim Assessment


Answer all questions QUESTION 1 During the last 20 years, KL's manufacturing operation has become increasingly automated with computer-controlled robots replacing operatives. KL currently manufactures over 100 products of varying levels of design complexity. A single, plant-wide overhead absorption rate (OAR), based on direct labour hours, is used to absorb overhead costs. In the quarter ended March 20X5, KL's manufacturing overhead costs were:

$000

Equipment operation expenses 125 Equipment maintenance expenses 25 Wages paid to technicians 85 Wages paid to storemen 35 Wages paid to despatch staff 40 ___ 310 ___

During the quarter, RAPIER Management Consultants were engaged to conduct a review of KL's cost accounting systems. RAPIER's report includes the following statement: In KL's circumstances, absorbing overhead costs in individual products on a labour hour absorption basis is meaningless. Overhead costs should be attributed to products using an activity based costing (ABC) system. We have identified the following as being the most significant activities: (1) Receiving component consignments from suppliers. (2) Setting up equipment for production runs. (3) Quality inspections. (4) Despatching goods orders to customers. Equipment operation and maintenance expenses are apportionable as follows: • Component stores (15%), manufacturing (70%) and goods despatch (15%).

Technician wages are apportionable as follows: • Equipment maintenance (30%), setting up equipment for production runs (40%) and

quality inspections (30%). During the quarter: • A total of 2,000 direct labour hours were worked (paid at $12 per hour). • 980 component consignments were received from suppliers. • 1,020 production runs were set up. • 640 quality inspections were carried out. • 420 goods orders were despatched to customers.



KL's production during the quarter included components r, s and t. The following information is available:

Component r Component s Component t

Direct labour hours worked 25 480 50 Direct material costs $1,200 $2,900 $1,800 Component consignments received

42

24

28

Production runs 16 18 12 Quality inspections 10 8 18 Goods orders despatched 22 85 46 Quantity produced 560 12,800 2,400

Required: (a) Calculate the unit cost of components r, s and t, using KL's existing cost accounting

system (single factory labour hour OAR). (4 marks) (b) Calculate the unit cost of components r, s and t, using this ABC system. (9 marks) (c) Explain the ideas concerning cost behaviour which underpin ABC. Explain why ABC

may be better attuned to the modern manufacturing environment than traditional techniques (7 marks)

(Total: 20 marks)

Interim Assessment


QUESTION 2 DFG manufactures two products from different combinations of the same resources. Unit selling prices and unit cost details for each product are as follows:

Product D G $/unit $/unit

Selling price 115 120 Direct material A ($5 per kg) 20 10 Direct material B ($3 per kg) 12 24 Skilled labour ($7 per hour) 28 21 Variable overhead ($2 per machine hour) 14 18 Fixed overhead* 28 36 Profit 13 11

*Fixed overhead is absorbed using an absorption rate per machine hour. It is an unavoidable central overhead cost that is not affected by the mix or volume of products produced. The maximum weekly demand for products D and G is 400 units and 450 units respectively and this is the normal weekly production volume achieved by DFG. However, for the next four weeks, the achievable production level will be reduced due to a shortage of available resources. The weekly resources that are expected to be available are as follows:

Direct material A 1,800 kg Direct material B 3,500 kg Skilled labour 2,500 hours Machine time 6,500 machine hours

Required: (a) Using graphical linear programming, identify the weekly production schedule for

products D and G that maximises the profits of DFG during the next four weeks. (15 marks) (b) The optimal solution to part (a) shows that the shadow prices of skilled labour and

direct material A are as follows:

Skilled labour $Nil Direct material A $5.82 Explain the relevance of these values to the management of DFG. (5 marks)

(Total: 20 marks)



QUESTION 3 MOC makes and sells two types of executive games, ‘Metropolis’ and ‘Hedge Your Bets’. The company currently has a monopoly for both games. This factor combined with the high quality of the games and the luxury brand image has resulted in MOC being able to charge high prices for each of the games. The management accountant is considering increasing the price for the Metropolis game and has produced the following information: At the current selling price of $55 per game, weekly sales of the Metropolis are 900 units. If the price is increased to $70 per game, weekly demand for the Metropolis will fall to 750 units. The Hedge Your Bets game is sold in two distinct markets. The management accountant believes that there should be price discrimination. The price is currently $80 per game in either market. Required: (a) Explain the term ‘price-discrimination’ and discuss the conditions that are necessary

for the successful operation of this pricing strategy. (4 marks) (b) Find the linear relationship between price (P) and quantity demanded (Q) for the

Metropolis game. (3 marks) (c) Calculate the price elasticity of demand (PED) for the Metropolis and comment on

whether the revenue will increase or decrease if the price is increased from $55 to $70 per game. (3 marks)

(d) Write a report to the management accountant to explain how the pricing strategy may

change if new competitors enter the market. Include, as part of your answer, a discussion of the different pricing strategies that may be implemented by MOC or its competitors. (10 marks)

(Total: 20 marks)

Interim Assessment


QUESTION 4 You are the management accountant of a publishing and printing company which has been asked to quote for the production of a programme for the local village fair. The work would be carried out in addition to the normal work of the company. Because of existing commitments, some weekend working would be required to complete the printing of the programme. A trainee accountant has produced the following cost estimate based upon the resources required as specified by the production manager:

$

Direct materials − paper (book value) 5,000 − inks (purchase price) 2,400 Direct labour − skilled 250 hours @ $4.00 1,000 − unskilled 100 hours @ $3.50 350 Variable overhead 350 hours @ $4.00 1,400 Printing press depreciation 200 hours @ $2.50 500 Fixed production costs 350 hours @ $6.00 2,100 Estimating department costs 400 ______ 13,150 ______

You are aware that considerable publicity could be obtained for the company if you are able to win this order, and the price quoted must be very competitive. The following notes are relevant to the cost estimate above: (1) The paper to be used is currently in stock at a value of $5,000. It is of an unusual

colour which has not been used for some time. The replacement price of the paper is $8,000, whilst the scrap value of that in stock is $2,500. The production manager does not foresee any alternative use for the paper if it is not used for the village fair programmes.

(2) The inks required are not held in stock. They would have to be purchased in bulk at a

cost of $3,000. 80% of the ink purchased would be used in printing the programmes. No other use is foreseen for the remainder.

(3) Skilled direct labour is in short supply, and to accommodate the printing of the

programmes, 50% of the time required would be worked at weekends, for which a premium of 25% above the normal hourly rate is paid. The normal hourly rate is $4.00 per hour.

(4) Unskilled labour is presently under-utilised, and at present 200 hours per week are

recorded as idle time. If the printing work is carried out at a weekend, 25 unskilled hours would have to occur at this time, but the employees concerned would be given two hours time off (for which they would be paid) in lieu of each hour worked.

(5) Variable overhead represents the cost of operating the printing press and binding

machines. (6) When not being used by the company, the printing press is hired to outside

companies for $6.00 per hour. This earns a contribution of $3.00 per hour. There is unlimited demand for this facility.



(7) Fixed production costs are those incurred by and absorbed into production, using an hourly rate based on budgeted activity.

(8) The cost of the estimating department represents time spent in discussions with the

village fair committee concerning the printing of its programme. Required: (a) Prepare a revised cost estimate using the opportunity cost approach, showing clearly

the minimum price that the company should accept for the order. Give reasons for each resource valuation in your cost estimate. (16 marks)

(b) Explain the relevance of opportunity costs in decision making. (4 marks) (Total: 20 marks)

Interim Assessment


QUESTION 5 QP is a food processing company that produces pre-prepared meals for sale to consumers through a number of different supermarkets. The company specialises in three particular pre-prepared meals and has invested significantly in modern manufacturing processes to ensure a high quality product. The company is very aware of the importance of training and retaining high quality staff in all areas of the company and, in order to ensure their production employees’ commitment to the company, the employees are guaranteed a weekly salary that is equivalent to their normal working hours paid at their normal hourly rate of $7 per hour. The meals are produced in batches of 100 units. Costs and selling prices per batch are as follows:

Meal TR PN BE

$/batch $/batch $/batch

Selling price 340 450 270

Costs:

Ingredient K ($5/kg) 150 120 90

Ingredient L ($10/kg) 70 90 40

Ingredient M ($15/kg) 30 75 45

Labour ($7/hour) 21 28 42

Factory costs absorbed 20 80 40

QP plc has adopted throughput accounting for its short-term decisions. Required: (a) State the principles of throughput accounting and the effects of using it for short-term decision making. (5 marks) (b) QP is preparing its production plans for the next three months and has estimated the maximum demand from its customers to be as follows:

TR 500 batches

PN 400 batches

BE 350 batches

These demand maximums are amended figures because a customer has just delayed its request for a large order and QP has unusually got some spare capacity over the next three months. However, these demand maximums do include a contract for the delivery of 50 batches of each to an important customer. If this minimum contract is not satisfied, then QP will have to pay a substantial financial penalty for non-delivery. The Production Director is concerned at hearing news that two of the ingredients used are expected to be in short supply for the next three months. QP does not hold inventory of these ingredients and, although there are no supply problems for ingredient K, the supplies of ingredients L and M are expected to be limited to:

Ingredient L 7,000 kilos

Ingredient M 3,000 kilos



The Production Director has researched the problem and found that ingredient V can be used as a direct substitute for ingredient M. It also costs the same as ingredient M. There is an unlimited supply of ingredient V. Required: Prepare calculations to determine the production mix that will maximise the profit of QP during the next three months and calculate the total throughput at this profit maximising point. (9 marks) (c) The World Health Organisation has now announced that ingredient V contains dangerously high levels of a chemical that can cause life-threatening illnesses. As a consequence it can no longer be used in the production of food. As a result, the production director has determined the optimal solution to the company’s production mix problem using linear programming. This is set out below:

Objective function value 110,714

TR value 500

PN value 357

BE value 71

TR slack value 0

PN slack value 43

BE slack value 279

L shadow price value 3

M shadow price value 28

Required: Briefly explain the meaning of each of the values contained in the above solution. (6 marks) (Total: 20 marks)

Interim Assessment

KAPLAN PUBLISHING Page 1 of 14

ACCA

Paper F5

Performance Management December 2009

Interim Assessment – Answers

To gain maximum benefit, do not refer to these answers until you have completed the interim assessment questions and submitted them for marking.


Page 2 of 14 KAPLAN PUBLISHING

© Kaplan Financial Limited, 2009 All rights reserved. No part of this examination may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without prior permission from Kaplan Publishing.

Interim Assessment


ANSWER 1

(a) Overhead absorption rate = activity of level Budgeted

overhead Budgeted

= hours 2,000

$310,000

= $155 per hour

Component r s t $ $ $

Labour 300 5,760 600 Material 1,200 2,900 1,800 Overhead 3,875 _____ 74,400 ______ 7,750 ______ 5,375 83,060 10,150 ÷ Number of units ÷ 560 _____ ÷ 12,800 ______ ÷ 2,400 ______ Cost per unit $9.60 _____ $6.49 ______ $4.23 ______

Working for Product r

Labour 25 hours × $12 = $300 Overhead 25 hours × $155 = $3,875

(b) Examination tip: Using the table below is of great benefit to show your work clearly.

Cost pool (1) (2) (3) (4) Total $000 $000 $000 $000

Equipment operation expenses (W1)

18.75

87.5

18.75

125.0

Equipment maintenance expenses (W1)

3.75

17.5

3.75

25.0 Technicians' wages (W2)

3.825

51.85

25.50

3.825

85.0

Storemen's wages 35.0 35.0 Despatch staff's wages

______

______

______

40.0 ______

40.0 ____

61.325 ______ 156.85 ______ 25.50 ______ 66.325 ______ 310.0 ____ ÷ Number of units ÷ 980 ÷ 1,020 ÷ 640 ÷ 420 Cost driver rate $62.58 $153.77 $39.84 $157.92 per

consignment per

set up per

inspection per

despatch



Working

(W1) Equipment operation expenses

$000 To cost pool (1) 15% of 125.0 = 18.75 To cost pool (2) 70% of 125.0 = 87.5 To cost pool (4) 15% of 125.0 = 18.75

Equipment maintenance expenses Apportioned to the cost pools as above. (W2) Technicians' wages

30% of 85.0 is apportioned to equipment maintenance, i.e. 25.5. This is then reapportioned to cost pools (1), (2) and (4).

(1) (2) (3) (4)

To cost pool (1); 15% of 25.5 3.825 To cost pool (2); 70% of 25.5 17.85 To cost pool (4); 15% of 25.5 3.825 Plus: 40% of 85.0 to cost pool (2) 34.0 30% of 85.0 to cost pool (3) _____ _____ 25.5 ____ _____ 3.825 _____ 51.85 _____ 25.5 ____ 3.825 _____

Component r s t $ $ $

Overheads Cost pool (1) 2,628 1,502 1,752 Cost pool (2) 2,460 2,768 1,845 Cost pool (3) 398 319 717 Cost pool (4) 3,474 ______ 13,424 ______ 7,265 ______ 8,960 18,013 11,579 Labour 300 5,760 600 Material 1,200 ______ 2,900 ______ 1,800 ______ Total cost 10,460 26,673 13,979 ÷ Number of units ÷ 560 ______ ÷ 12,800 ______ ÷ 2,400 ______ Cost per unit $18.68 ______ $2.08 ______ $5.82 ______

Interim Assessment


Working for Product r Cost pool (1) 42 × $62.58 = $2,628 Cost pool (2) 16 × $153.77 = $2,460 Cost pool (3) 10 × $39.84 = $398 Cost pool (4) 22 × $157.92 = $3,474

(c) ABC is based upon the idea that overhead costs vary with support activities associated with manufacturing.

ABC sets out to understand which factors cause the cost to vary (cost driver) and to

then charge overheads to products on the basis of the consumption of their support activities.

There have been two major changes in the modern manufacturing environment over

the last two decades:

(1) Due to automation of production, labour costs of a firm have reduced significantly. As a consequent of this, overhead costs now form a far greater proportion of a firm's total costs than previously. Because of this, it has become increasingly important for a company to understand and be able to control its overheads effectively.

(2) Many companies are now full-line multi-product manufacturers – producing a

wide variety of product lines. This has lead to manufacturing techniques and scheduling becomes vastly more complicated than in previous decades. As the manufacturing process has become more complicated, associated overheads have increased, for example material purchasing, material handling, quality inspections, order despatch, batch set ups, etc.

ABC aims to recognise these changes. This is in contrast to the more traditional approach which charges overheads to production using a volume based overhead absorption rate. For example, a traditional approach to charging overheads to products would be on a direct labour hour rate. Effectively, this method assumes that overheads are related to direct labour hours. Professors Cooper and Kaplan (the chief advocates of ABC) argue that overheads are rarely related to labour hours, so a volume based OAR such as this is meaningless.

MARKING GUIDE

Marks

(a) OAR 1 Cost of each product, 1 mark each 3 (b) 4 cost driver rates, 1½ marks each 6 Cost of each product, 1 mark each 3 (c) Cost behaviour of ABC costs 3 Why ABC is attuned to modern environment 4 __ Total 20

__



ANSWER 2 (a) Profit will be maximised by maximising contribution. Fixed costs do not vary with quantity produced and are therefore not relevant to the

decision.

Let: d = quantity of product D produced g = quantity of product G produced Contribution per unit of product D = Selling price − Variable cost = $115 − $(20 + 12 + 28 + 14) = $41 Contribution per unit of product G = Selling price − Variable cost = $120 − $(10 + 24 + 21 + 18) = $47

Product D Product G

Contribution/unit ($) 41 47 Usage of material A/unit (kg) 20/5 = 4 10/5 = 2 Usage of material B/unit (kg) 12/3 = 4 24/3 = 8 Usage of skilled labour/unit (hours) 28/7 = 4 21/7 = 3 Usage of machine/unit (hours) 14/2 = 7 18/2 = 9 Maximum weekly demand (units) 400 450

Objective function Contribution C = 41d + 47g Constraints: Material A 4d + 2g ≤ 1,800 Material B 4d + 8g ≤ 3,500 Skilled labour 4d + 3g ≤ 2,500 Machine hours 7d + 9g ≤ 6,500 d ≤ 400 g ≤ 400 d ≥ 0 g ≥ 0 Plotting these lines on the graph: Material A: d = 0, g = 900 d = 450, g = 0

Interim Assessment


Material B: d = 0, g = 437.5 d = 75, g = 400 d = 875, g = 0 Skilled labour: d = 250, g = 500 d = 400, g = 300 d = 0, g = 833.33 d = 625, g = 0 Machine hours: d = 0, g = 722.22 d = 928.57, g = 0 To plot iso-contribution line: Say C = 19,270 = 41d + 47g, then: d = 0, g = 410 d = 470, g = 0 From the graph, contribution will be maximised on the iso-contribution line furthest from the origin which touches the edge of the feasible region and is furthest from the origin. This point, point P, is at the intersection of the constraint lines for material A and material B. This point is the solution of the simultaneous equations: (1) 4d + 2g = 1,800 and (2) 4d + 8g = 3,500 Subtracting equation (1) from equation (2): 6g = 1,700 g = 283 units and substituting this in (1): 4d + 2 × 283 = 1,800 4d = 1,234 d = 308 units Weekly production schedule to maximise contribution = 308 units of D and 283 units of G.



(b) The shadow price of a resource is an increase in value which would be created by

having available one additional unit of a limiting resource at its original cost. This means that there would be an increase in value of $5.82 for every unit of material A which is available. However, there will be no increase in value if additional skilled labour as it has a shadow price of $Nil and availability of skilled labour is not a binding constraint at the optimum solution. It can be seen from the graph that this is indeed the case as the constraint line for the skilled labour lies outside the feasible region.

Shadow prices (also known as opportunity costs or dual prices) are one of the most important aspects of linear programming.

Interim Assessment


• The shadow price is the extra profit that may be earned by relaxing each of the constraints by one unit.

• It therefore represents the maximum premium that the firm should be willing to pay for one extra unit of each constraint. In the case of material A the firm should be willing to pay $5.82 for each additional unit of material A.

• Since shadow prices indicate the effect of a one unit change in each of the constraints, they provide a measure of the sensitivity of the result.

MARKING GUIDE

Marks

(a) Establish and plot constraints 12 Identify iso-contribution line 2 Identify optimal plan 1 (b) General explanation of shadow price 1 Shadow price of skilled labour 2 Shadow price of material A 2 __ Total 20 __



ANSWER 3 (a) A price-discrimination strategy is where a company sells the same products at different prices in different markets. Three conditions are necessary for the successful operation of this pricing strategy:

1. The seller must be able to determine the selling price. MOC has a monopoly and therefore this would be possible.

2. It must be possible to segregate customers into different markets, e.g. using geographical location or age.

3. Customers must not be able to but at the lower price in one market and sell at the higher price in another market.

(b) 1. The equation of a straight line is: y = a + bx

where y = price (P) a = intersection of the line with the y-axis b = gradient x = quantity (Q)

2. Start by calculation the gradient (b):

Gradient = 700- 900quantity in Change

$70-$55 price in Change = -0.1

3. Using the price of $55, this gradient can be substituted back into the

equation:

y = a + bx 55 = a – (0.1 × 900) 55 = a – 90 a = 55 + 90 a = 145

(Alternatively: the price of $70 could be substitutes back into the equation).

4. Therefore the linear relationship is P = 145 – 0.1Q

(c) PED = price in change %

demand in change %

= 100 (15/55)

100 (-150/900)×

×

= 27.27%-16.67%

= -0.611 = 0.611 (sign can be ignored)

The PED is less than 1 and as a result demand is inelastic. Therefore increasing the price from $55 to $70 will increase the revenue.

Interim Assessment


(d) To: Management Accountant From: Student Date: xx/xx/xx

The current pricing strategy may not be able to be applied if competition was to emerge in the market as the business would now have to be more aware of the competitors' prices. We may be forced to use going rate pricing to match the competitors prices to compete. However they may choose to adopt a penetration pricing strategy, which means that they will start off with a low price to try and gain some of our market share. Competing at this price will drive down are profit margins, however we may be able to sustain low margins in the short term to try and hold onto our customer base. As we have had such a strong monopoly of the market we should already have sufficient economies of scale to be able to withstand the lower profit margins for longer than the competitor. And may even be able to undercut them so that they can not gain any of market share. Alternatively, as we are already an established name in the market we may be able to rely on brand loyalty and keep our prices high. By keeping a high price our customer may also perceive our product to be of higher quality. This could work particularly well because this is an executive game and presumably the customer would be more likely to choose quality over a lower price.

MARKING GUIDE

Marks (a) Definition 1 1 mark for each condition up to a maximum of 3 (b) Correct gradient 1 Correct intersection 1 Correct linear relationship 1 (c) Correct PED calculation 2 Correct revenue conclusion 1 (d) Report format and good presentation 1 1 Mark for each relevant comment 9 __ Total 20 __



ANSWER 4 Suggested answer

(a) Reasons $

Paper − Book value is irrelevant because it is a sunk cost; as there is no other use, replacement would not occur so the opportunity cost or scrap sale proceeds is the relevant value.

2,500

Ink − Since this involves a future cost if the work is undertaken, the purchase price should be used. Since the remaining stock has no foreseeable use it has no value so the entire purchase cost is used.

3,000

Skilled labour − Since the weekend working is caused if the work is undertaken, the full cost is relevant: 125 hours @ $4/hr = $500 125 hours @ $5/hr = $625

1,125

Unskilled labour

− The weekend work results in 50 hours time off in lieu − this, with the 75 other hours worked, totals 125 hours, which is less than the 200 hours of idle time which are already being paid for; thus there is no incremental cost.

Nil

Variable overhead

− This is a future cost which will be incurred if the work is undertaken.

1,400

Printing press − The depreciation is a past cost and should be ignored, however the use of the press has an opportunity cost. If this work is undertaken, then the press is not available for hire. The opportunity cost is the contribution which would be earned from hiring:

200 hours @ ($6 − $3) 600

Production fixed costs

− As these costs are unaffected by the decision they should be ignored

Nil

Estimating costs

− These costs are past or sunk costs and should be ignored.

Nil

______ MINIMUM PRICE £8,625 ______

(b) An opportunity cost is the value which represents the cost of the next best alternative or the benefit forgone by accepting one course of action in preference to others when allocating scarce resources.

If there is only one scarce resource, decisions can be made by ranking alternatives according to their contributions per unit of the scarce resource. However, in reality, there will be many scarce resources, and different alternatives will use alternative combinations of those scarce resources. In these situations, opportunity costs are used to identify the optimum use of those resources.

MARKING GUIDE Marks (a) 2 marks per cost type with explanation 16 (b) Definition of opportunity cost 1 Scarce resources 1 Relevant costs 2 Total 20 __

Interim Assessment


ANSWER 5 (a) Throughput accounting is based on the assumption that all costs except material are fixed and throughput can be calculated as sales price less material costs. It can be seen that this is a similar measure to contribution, except that in traditional analysis labour is normally considered to be a variable cost. Throughput accounting’s primary concern is the rate at which a business generates profits and a company will wish to maximise throughput. This is measured using the return per period ratio. This ratio can also be used in short-term decision making to calculate an optimal production mix. A return per bottleneck resource is calculated for each product and ranked in a similar way to limiting factor analysis. This ranking can then be used to select the product which produces the greatest throughput per unit of the bottleneck resource.

(b) QP uses throughput accounting for short-term decisions, so first calculate contribution assuming material is the only variable cost. Ingredient L is the limiting factor.

TR PN BE

Sales price 340 450 270

Materials 250 285 175

––– ––– –––

Throughput 90 165 95

Kgs of L 7 9 4

Throughput per kg of L $12.86 $18.33 $23.75

Rank 3 2 1

Production plan (maximum of 7,000kg of L available):

First allocate minimum contract

50 TR × 7 350

50 PN × 9 450

50 BE × 4 200

–––––

1,000

Next produce BE to maximum demand

300 × 4 1,200

Then PN to maximum demand

350 × 9 3,150

–––––

5,350

Produce TR with the 1,650 kgs remaining

235 × 7 1,645

–––––

6,995



(Not enough L left to produce another full batch of TR.) The production plan to maximise the profit of QP is:

Total throughput

350 BE × $90 31,500

400 PN × $165 66,000

285 TR × $95 27,075

–––––––

$124,575

(c) The objective function value of 110,714 represents the maximum throughput which can be earned given the new constraint. This represents a fall of $13,861 compared to the optimal solution calculated in (b). The throughput is achieved by producing 500 batches of TR, 357 batches of PN and 71 batches of BE. The slack variables show the extent that this represents a shortfall on the maximum demand achievable. Thus the maximum demand of 500 batches of TR is produced (0 slack variable), a shortfall of 43 batches of PN (357 + 43 = 400) and a shortfall of 279 units of BE (71 + 279 = 350). The shadow price L value of $3 represents the amount of extra throughput which could be earned if there was one more kg of L available. The shadow price M value represents the amount of extra throughput which could be earned if there was one more kg of M available

MARKING GUIDE

Marks

(a) 1 mark for each relevant point. 5

(b) Identification of limiting factor 1 Calculation of throughput per unit 1 Calculation of throughput/ kg of L 1 Rank 1 Optimum production plan 3 Maximum throughput 2 9 (C) Each relevant point 1 6 __ Total 20 __

f5 interim

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