PPM 3-2

1. NEON PHARMACEUTICALS

Neon Pharmaceuticals is a research-based company which manufactures a wide variety of drugs for use in hospitals. The purchasing manager has recently been approached by a new manufacturer based in a newly industrialised country who has offered to produce three of the drugs at their factory. The following cost and price information has been provided.

Drug                                                           Fairyoxide                    Spriteolite                          Goblinex

Production (units)                                      20,000                           40,000                               80,000

$                                     $                                         $

Direct material cost, per unit                     0.80                               1.00                                   0.40

Direct labour cost, per unit                        1.60                               1.80                                   0.80

Direct expense cost, per unit                     0.40                               0.60                                   0.20

Fixed cost per unit                                       0.80                               1.00                                   0.40

Selling price each                                         4.00                               5.00                                   2.00

Imported price                                             2.75                               4.20                                   2.00

I. What saving/(increased cost) per unit would be made/(incurred) if Fairyoxide was purchased from the overseas producer (to two decimal places)?

II. What profit will the company make by producing all the drugs itself?

III. The following two statements have been made about the decision Neon Pharmaceuticals has to make about producing the products in house or purchasing from the overseas producer.

Are they true or false?

A. In a make-or-buy decision with no limiting factors, the relevant costs are the differential costs between the make and buy options.

B. Cost is the only relevant factor in Neon Pharmaceutical’s make-or-buy decision.

IV. What saving/(increased cost) would be made/(incurred) if Goblinex was purchased from the overseas producer?

V. What saving/(increased cost) would be made/(incurred) per unit if Spriteolite was purchased from the overseas producer?

2. DD CO

DD Co is launching a new, innovative product (a computer game) onto the market and is trying to decide on the right launch price for the product.

The product’s expected life is three years. Given the high level of costs which have been incurred in developing the product, DD Co wants to ensure that it sets its price at the right level and has therefore consulted a market research company to help it do this.

The research, which relates to similar but not identical products launched by other companies, has revealed that at a price of $60, annual demand would be expected to be 250,000 units. However, for every $2 increase in selling price, demand would be expected to fall by 2,000 units and for every $2 decrease in selling price, demand would be expected to increase by 2,000 units. A forecast of the annual production costs which would be incurred by DD Co in relation to the new product are as follows:

I. What are the total fixed overheads?

II. Using the high-low method, what is the total variable cost per unit?

III. If the marginal cost is $21, what is the optimum (profit maximising) selling price for the new product?

IV. DD’s game is truly unique and can only be used in conjunction with another one of the business’ products. Students are entitled to a small discount.

Which of the following pricing strategies could be used to price the game?

(1) Market skimming.

(2) Complimentary product pricing.

(3) Penetration pricing.

(4) Price discrimination.

V. The sales director is unconvinced that using an optimum (profit-maximising) selling price is the correct one to charge at the initial launch of the product. He believes that a high price should be charged at launch to take advantage of those customers prepared to pay a higher price for the product.

Which TWO of the following statements are true?

(1) The sales director is suggesting a market skimming strategy.

(2) The strategy could be a suitable one for DD Co as its product is new and different.

(3) Where products have a long life cycle, this strategy is more likely to be used.

(4) There is no barrier to entry in the case of DD Co.

3. ELECTRO CO

Electro Co sells electronic equipment and is about to launch a new product onto the market. It needs to prepare its budget for the coming year and is trying to decide whether to launch the product at a price of $30, or $35 per unit. The following information has been obtained from market research:

The six possible profit outcomes which could arise for Electro Co in the coming year have been correctly tabulated as follows:

I. Which is the correct definition of the maximin decision rule?

II. What is the expected value of profit for the $35 price option?

III. What is the expected value of profit for the $30 price option?

IV. Which price should be chosen by management if they use the maximax rule to decide which price should be charged?

V. Which price should be chosen by management if they use the maximin rule to decide which price should be charged?

4. DONALD

Donald has been asked to quote a price for a one-off contract. The company’s management accountant has asked for your advice on the relevant costs for the contract. The following information is available:

Materials

The contract requires 3,000 kg of material W, which is a material used regularly by the company in other production. The company has 2,000 kg of material W currently in inventory which had been purchased last month for a total cost of $19,600. Since then, the price per kilogram for material W has increased by 5%.

The contract also requires 200 kg of material X. There are 250 kg of material X in inventory which are not required for normal production. This material originally cost a total of $3,125. If not used on this contract, the inventory of material X would be sold for $11 per kg.

Labour

The contract requires 800 hours of skilled labour. Skilled labour is paid $9.50 per hour. There is a shortage of skilled labour, and all the available skilled labour is fully employed in the company in the manufacture of product Z. The following information relates to product Z:

$ per unit                    $ per unit

Selling price                                                                                    100

Less:

Skilled labour                                             38

Other variable costs                                 22

(60)

40

Finance costs

In order to complete the contract, a member of the finance team will be required to work eight hours overtime. The individual’s annual salary is $25,000, and they work a 37.5 hour week. Overtime is paid at a rate of $15 per hour. Alternatively, an experienced contract accountant can be hired to administer the project in 75% of the time it would take the internal finance department member to complete. The contractor’s rate is $25 per hour. It took the member of the finance team three hours to put together the information for this quote and no overtime was required.

I. What is the relevant cost of material X which should be included in the contract?

II. What is the relevant cost of material W which should be included in the contract?

III. What is the relevant cost of finance which should be included in the contract?

IV. Are the following statements about Donalds’s relevant costing system true or false?

A. Sunk costs can never be a relevant cost for the purpose of decision-making.

B. Fixed overhead costs can never be a relevant cost for the purpose of decision-making.

V. What is the relevant cost of skilled labour which should be included in the contract?

5. SHIP CO

Ship Co specialises in refurbishing the inside of yachts and has been asked to quote, on a relevant cost basis, for the refurbishment of a yacht called Bow. The refurbishment will start in one week’s time. Ship Co has spent $100 obtaining the following information about the refurbishment:

Materials

The material required will be:

• 20 m² of upholstery fabric
• 10 m² of teak wood for the flooring

The cheapest source for the upholstery fabric would be from an overseas supplier at a cost of $85/m². Ship Co buys most of its fabric from overseas and pays $400 per month to a shipping company as a retainer and then $7.50/m² for each metre transported.

Ship Co has 5m² of teak wood in inventory which cost $100/m² and could be sold at a 5% discount on original cost. This teak is left from a previous job and is stained dark mahogany. The colour of the stain required for Bow, tan, is lighter and the costs of sanding and staining the teak are:

• sanding $14/m²
• staining $4.50/m²
• reset of staining machine, arising after each staining job is completed $80.

To ensure the colour of the teak is consistent, all the teak for one job is stained at the same time, and the staining cost is the same irrespective of the age of the teak. The cost of purchasing new teak is $110/m². New teak can be stained the correct colour for Bow with no preparation.

Non-current assets

A new kitchen will be required. This can be purchased for $4,500 and the fitting costs will be $2,000. Alternatively, the existing kitchen can be refurbished. The materials for refurbishment will cost $4,000, and 40 hours of semi-skilled labour will be employed specifically for the refurbishment at a cost of $15/hour. The fitting costs of the refurbished kitchen will be 10% less than a new kitchen.

Labour

100 hours of skilled and 56 hours of unskilled labour will be required for the upholstery and flooring work. Skilled labour is paid the market rate of $25/hour and is currently fully employed on another job, where they earn a contribution of $6/hour. Alternatively new skilled labour could be employed, but the new workers will require training at a cost of $14/hour for the first 10 hours they are working.

Unskilled workers are currently paid $12/hour and each of the 5 workers is guaranteed a minimum wage of $420 per week. Each unskilled employee has enough work allocated to them for the next three weeks to earn $372 per week. The work to be done by the unskilled labour on Bow must be completed within the first week of the project starting and overtime is paid at time and half.

Other costs

It is factory policy to add $2,200 per week to a project, for the duration of the project. This is to cover:

I. What cost should be included in the quote for the teak wood?

II. What are the costs to be included in the quote for the upholstery fabric and kitchen?

Upholstery fabric

$ Kitchen

III. Which option correctly classifies these costs? Choose the appropriate box in the table below.

A. Factory rates

B. Depreciation

C. Interest

IV. What cost should be included in the quote for the skilled and unskilled labour?

Skilled labour

$ Unskilled labour

V. Which TWO of the following statements are true?

6. LITTLE CO

Little Co is a manufacturer of baby equipment and is planning to launch a revolutionary new style of sporty pushchair. The company has commissioned market research to establish possible demand for the pushchair and the following information has been obtained.

If the price is set at $425, demand is expected to be 1,000 pushchairs; at $500 it will be 730 pushchairs and at $600 it will be 420 pushchairs. Variable costs are estimated at $170, $210 or $260.

A decision needs to be made on what price to charge.

The following contribution table has been produced showing the possible outcomes.

I. What price would be set if Little Co were to use a minimax regret decision criterion?

II. What price would be set if Little Co were to use a maximin decision criterion?

III. Which TWO of the following, used by Little Co, reduce uncertainty in decision-making?

IV. If the probabilities of the variable costs are $170: 0.4; $210: 0.25; and $260: 0.35, which price would the risk-neutral decision maker choose?

V. Indicate, by selecting the relevant boxes in the table below, whether each of the following statements regarding Little Co’s use of expected values is correct or incorrect.

A. Expected-value analysis is suitable for risk-averse decision makers, as all likely outcomes are presented.

B. The average profit calculated will correspond to one of the possible outcomes.

7. HC CO

HC Co manufactures four types of fitness equipment: elliptical trainers (E), treadmills (T), cross trainers (C) and rowing machines (R). HC Co is considering ceasing to produce elliptical trainers at the end of 20X5.

The budgeted sales prices and volumes for the next year (20X6) are as follows:

T                           C                           R

Selling price                                      $1,600                 $1,800                  $1,400

Units                                                      420                      400                        380

Total sales revenue                       $672,000            $720,000              $532,000              $1,924,000

The standard cost card for each product is shown below:

Labour costs are 60% fixed and 40% variable. General fixed overheads excluding any fixed labour costs are expected to be $55,000 for the next year.

The following multi-product breakeven chart for HC Co has correctly been drawn:

HC Co has recently received a request from a customer, LH Co, to provide a one-off order of fitness machines (T, C and R), in excess of normal budgeted production for 20X6. The order would need to be completed within two weeks.

I. What is the margin of safety in $ revenue for HC Co in 20X6?

II. Which of the following are valid factors to consider in the decision to cease the production of elliptical trainers at the end of 20X5?

(1) The elliptical trainers made a loss in 20X5.

(2) The elliptical trainers made a positive contribution in the year just passed.

(3) The elliptical trainer market outlook in the long term looks very poor.

(4) HC Co also sells treadmills and many elliptical trainers buyers will also buy treadmills.

(5) The business was founded to produce and sell elliptical trainers.

III. What would happen to the breakeven point if the products were sold in order of the most profitable products first?

IV. Which of the following statements about relevant costing are true?

(1) Fixed costs are always general in nature and therefore never relevant.

(2) Notional costs are always relevant, as they make the estimate more realistic.

(3) An opportunity cost represents the cost of the best alternative foregone.

(4) Avoidable costs would be saved if an activity did not happen, and therefore are relevant.

V. Which statement correctly describes the treatment of general fixed overheads when preparing the LH Co quotation?

8. JENNY CO

Jenny Co is an engineering company that manufactures a number of products, using a team of highly skilled workers and a variety of different metals. A supplier has informed Jenny Co that the amount of M1, one of the materials used in production, will be limited for the next three-month period.

The only items manufactured using M1 and their production costs and selling prices (where applicable) are shown below.

Product P4                       Product P6

$/unit                               $/unit

Selling price                                          125                                    175

Direct materials:

M1*                                                        15                                      10

M2                                                          10                                      20

Direct labour                                        20                                      30

Variable overhead                               10                                      15

Fixed overhead                                    20                                      30

Total cost                                              75                                     105

* Material M1 is expected to be limited in supply during the next three months. These costs are based on M1 continuing to be available at a price of $20 per square metre. The price of M2 is $10 per square metre.

I. What is the contribution per unit for each product?

A.

B.

II. Indicate, by selecting the relevant boxes in the table below, whether each of the following costs would be included in the calculation of throughput contribution if Jenny Co operated in a throughput accounting environment.

A. Selling price

B. Direct materials

C. Direct labour

III. Jenny Co carried out some market research which suggested that a change should be made to the selling price of both Product P4 and P6. As a result, the new contribution per unit for P4 is $85 and for P6 it is $95. Which of the following answers is correct?

IV. Indicate, by selecting the relevant boxes below, which of the following constraints would necessitate the performance of limiting factor analysis by Jenny Co.

V. Once a scarce resource is identified, Jenny Co carries out a limiting factor analysis using four steps. Match each of the steps to the correct order in which they should be carried out.

A. Rank the products in order of the contribution per unit of the scarce resource.

B. Allocate resources using the ranking.

C. Calculate the contribution per unit of the scarce resource for each product.

D. Calculate the contribution per unit for each product.

9. TEE EVENTS

Tee Events is a company which specialises in organising sporting events in major cities across Teeland. It has approached the local council of Edglas, a large city in the north of Teeland, to request permission to host a running festival which will include both a full marathon and a half marathon race.

Based on the prices it charges for entry to similar events in other locations, Tee Events has decided on an entry fee of $55 for the full marathon and $30 for the half marathon. It expects that the maximum entries will be 20,000 for the full marathon and 14,000 for the half marathon. Tee Events has done a full assessment of the likely costs involved. Each runner will receive a race pack on completion of the race which will include a medal, t-shirt, water and chocolate. Water stations will need to be available at every five kilometre (km) point along the race route, stocked with sufficient supplies of water, sports drinks and gels. These costs are considered to be variable as they depend on the number of race entries.

Tee Events will also incur the following fixed costs. It will need to pay a fixed fee to the Edglas council for permits, road closures and support from the local police and medical services. A full risk assessment needs to be undertaken for insurance purposes. A marketing campaign is planned via advertising on running websites, in fitness magazines and at other events Tee Events is organising in Teeland, and the company which Tee Events usually employs to do the race photography has been approached.

The details of these costs are shown below:

Full marathon                    Half marathon

$                                           $

Race packs                                                                                    15.80                                   10.80

Water stations                                                                               2.40                                     1.20

$

Council fees                                                                                                                             300,000

Risk assessment and insurance                                                                                             50,000

Marketing                                                                                                                                 30,000

Photography                                                                                                                              5,000

I. If Tee Events decides to host only the full marathon race, what is the margin of safety?

II. Tee Events wishes to achieve a minimum total profit of $500,000 from the running festival.

What are the number of entries Tee Events will have to sell for each race in order to achieve this level of profit, assuming a constant sales mix based on the expected race entry numbers applies?

Work to the nearest whole number.

III. Assuming that the race entries are sold in a constant sales mix based on the expected race entry numbers, what is the sales revenue Tee Events needs to achieve in order to break even (to the nearest $000)?

IV. Which of the following statements relating to cost volume profit analysis are true?

(1) Production levels and sales levels are assumed to be the same so there is no inventory movement.

(2) The contribution to sales ratio (C/S ratio) can be used to indicate the relative profitability of different products.

(3) CVP analysis assumes that fixed costs will change if output either falls or increases significantly.

(4) Sales prices are recognised to vary at different levels of activity especially if higher volume of sales is needed.

V. Tee Events is also considering including a 10 km race during the running festival. It expects the race will have an entry fee of $20 per competitor and variable costs of $8 per competitor. Fixed costs associated with this race will be $48,000.

If the selling price per competitor, the variable cost per competitor and the total fixed costs for this 10 km race all increase by 10%, what will happen to the breakeven volume and the breakeven revenue? Choose the appropriate box in the table below.

A. Breakeven volume

B. Breakeven revenue

10. LOITO CO

Loito Co is a company specialising in the provision of telephone systems for commercial clients.

Loito Co has been approached by a potential customer, Stim Co, which wants to install a telephone system in new offices it is opening. While the job is not a particularly large one, Loito Co is hopeful of future business in the form of replacement systems and support contracts for Stim Co. Loito Co is therefore keen to quote a competitive price for the job. The following information should be considered:

• One of the company’s salesmen has already been to visit Stim Co, to give them a demonstration of the new system, together with a complimentary lunch, the costs of which totalled $400.
• The installation is expected to take one week to complete and would require three engineers, each of whom is paid a monthly salary of $4,000. The engineers have just had their annually renewable contract renewed with Loito Co. One of the three engineers has spare capacity to complete the work, but the other two would have to be moved from Contract K in order to complete this one. Contract K generates a contribution of $200 per engineer per week. There are no other engineers available to continue with Contract K if these two engineers are taken off the job. It would mean that Loito Co would miss its contractual completion deadline on Contract K by one week. As a result, Loito Co would have to pay a one-off penalty of $500. Since there is no other work scheduled for their engineers in one week’s time, it will not be a problem for them to complete Contract K at this point.
• 120 telephone handsets would need to be supplied to Stim Co. The current cost of these is $18.20 each, although Loito Co already has 80 handsets in inventory. These were bought at a price of $16.80 each. The handsets are the most popular model on the market and are frequently requested by Loito Co’s customers.
• Stim Co would also need a computerised control system called ‘Swipe 2’. The current market price of Swipe 2 is $10,800, although Loito Co has an older version of the system, ‘Swipe 1’, in inventory, which could be modified at a cost of $4,600. Loito Co paid $5,400 for Swipe 1 when it ordered it in error two months ago and has no other use for it. The current market price of Swipe 1 is $5,450, although if Loito Co tried to sell the one it has, it would be deemed to be ‘used’ and therefore only worth $3,000.

I. What figure should be included in the relevant cost statement for telephone handsets?

II. What figure should be included in the relevant cost statement for engineers’ costs?

III. What is the type of cost that is detailed in point 1)?

IV. What figure should be included in the relevant cost statement for the computerised control system?

V. Indicate, by selecting the relevant boxes in the table below, whether each of the following statements about Loito Co’s decision to quote for the contract are true or false?

A. The decision to install the telephone system should be taken purely on the basis of whether it improves profit or reduces costs for Loito Co.

B. The opportunity cost is defined as the relevant cost of taking a business opportunity to install the telephone system for Stim Co.

11. MELBON CO

Melbon Co makes two products, Seebach (S) and the Herdorf (H).

To make a unit of each product the following resources are required:

S                                    H

Materials ($100 per kg)                                                              5 kg                               7 kg

Labour hours ($45 per hour)                                                  2 hours                         3 hours

Machine hours ($60 per hour)                                               3 hours                         2 hours

Fixed overheads are $300,000 each month.

The contribution per unit made on each product is as follows:

S                                     H

Contribution ($ per unit)                                                           250                                 315

The maximum demand each month is 4,000 units of S and 3,000 units of H. The products and materials are perishable and inventories of raw materials or finished goods cannot be stored.

Melbon Co has a legally binding obligation to produce a minimum of 2,000 units of H in each of months 1 and 2. There is no minimum production required in month 3.

The manufacturing manager is planning production volumes and the maximum availability of resources for months 1, 2 and 3 are as follows:

Month                                            1                            2                            3

Materials (kg)                          34,000                  42,000                  35,000

Labour (hours)                        18,000                  12,000                  24,000

Machine (hours)                     18,000                  19,000                  12,000

 For month 3 the following linear programming graph has been produced:

I. What is/are the limiting factor(s) in month 1?

II. If the shadow price for month 2 is $125 per labour hour, which of the following statements is/are correct?

(1) The production manager would be willing to pay existing staff a maximum overtime premium of $125 per hour for the next 2,000 hours.

(2) The production manager would be willing to pay a maximum of $170 per hour for an additional 2,000 hours of temporary staff time.

III. The production manager has identified that the only limiting factor in month 2 is labour hours.

What is the production volume for Herdorf for month 2 (to the nearest whole unit)?

IV. Which of the following interpretations of the linear programming graph produced for month 3 is/are correct?

(1) All other things being equal, unless demand increases for either product labour will be a slack variable.

(2) If more machine hours were made available in month 3, they would be used initially to make Herdorfs.

V. What is the maximum profit which can be earned in month 3?

12. PM CO

PM Co manufactures mobile phones. It has been extremely successful in the past, but the market has become extremely competitive. The company is considering a number of different strategies to improve its profitability.

The most successful product is the PM55 which is sold for $110. Weekly demand is currently 20,000 phones. Market research has revealed that if PM Co reduced the price of the PM55 by $10, demand would increase by 2,000 phones.

Each time the phone is produced, PM Co incurs extra costs of $30 for materials, $18 for labour, $14 for variable overheads and $23 for fixed costs, based on expected weekly output of 20,000 phones. The most expensive component in the phone is the battery which costs $15.

PM Co has been offered a discounted price of $12 by the supplier if it buys 22,000 batteries per week.

I. When is a market penetration pricing policy appropriate for PM Co?

II. What is the straight line demand equation for the PM55?

P =  ____(A)____  –  ______(B)______ Q

A. 

B. 

III. What is the total cost function for the PM55 after the volume discount?

TC =  ____(A)____  +  ______(B)______ Q

A.

B.

IV. What is the total cost function for the PM55 before the volume discount?

TC =  ____(A)____  +  ______(B)______ Q

A.

B. 

V. PM Co produces another phone with a price elasticity of demand equal to one.

Indicate, by selecting the relevant boxes in the table below, whether each of the following statements are true or false.

A. Demand will remain constant despite price changes.

B. If price increases by 5%, demand will fall by 10%.

C. Total expenditure will remain constant despite price changes.

13. STEVE CO

Steve Co is setting up an online business importing and selling jewellery headphones. The cost of each set of headphones varies depending on the number purchased, although they can only be purchased in batches of 1,000 units. It also has to pay import taxes which vary according to the quantity purchased.

Steve Co has already carried out some market research and identified that sales quantities are expected to vary depending on the price charged. Consequently, the following data has been established for the first month:

Most of Steve Co’s total fixed costs are set-up costs.

Earphones

Steve Co is also producing luxury earphones and has entered two different new markets. In the USA, it is initially charging low prices so as to gain rapid market share while demand is relatively elastic. In Europe, it is initially charging high prices so as to earn maximum profits while demand is relatively inelastic.

Market research has revealed that the maximum demand for Steven Co’s earphones in the USA is 72,000 units per year, and that demand will reduce by 8,000 units for every $5 that the selling price is increased. Steve Co has calculated that the profit-maximising level of sales for its earphones, for the coming year, is 32,000 units.

I. Which of the following statements(s) regarding Steve Co’s fixed costs is/are correct?

(1) Steve Co’s fixed costs are stepped.

(2) Increasing batch sizes from 1,000 units to 2,000 units would dramatically reduce setup costs and increase profits.

II. How many batches should Steve Co import and sell (to the nearest whole batch)?

III. What is the optimum selling price at the profit-maximising level of sales (to the nearest $)?

IV. Which price strategy is Steve Co using in each market?

V. The following statements have been made about the tabular method used to establish an optimum price:

Which of the following statement(s) regarding Steve Co’s fixed costs is/are correct?

(1) With the tabular method, there must be a consistent relationship between price (P) and demand (Q), as well as a close relationship between demand (Q) and marginal costs (MC).

(2) The tabular method is only suitable for companies operating in a monopoly.

14. WHITE CO

White Co makes plates. Three different styles of plates are made, and the following information is available:

Painting labour is limited to 7,250 hours a week for the next month, while some of the workers are away on a training course.

1. What is the production plan that would maximise profit for the next month?

Square                       Oval                     Clover Leaf

A                    1,000                        4,500                             –

B                    4,000                        3,500                             –

C                    4,000                        1,100                         1,800

D                        –                            4,500                           250

II. Which TWO of the following statements about limiting factor analysis are true?

III. White Co is considering permanently ceasing production of the clover leaf plates.

Which TWO of the following factors should be considered in this decision?

(1) The head office costs apportioned to the clover leaf plates.

(2) The decommissioning costs for the clover leaf plate.

(3) The budget for clover leaf plates shows a loss for next year.

(4) The impact on reputation of reducing the range of plates produced by White Co.

IV. White Co does not want to disappoint any customers next week and is considering sub-contracting out some painting, even if it results in a short term loss. The cost of contracting out (which includes material costs and labour costs for painting) would be:

A major customer, B Co, who orders 500 of each type of plates each week insists that their plates are painted in-house and not sub-contracted.

How many oval plates should be sent to the sub-contractors for painting?

V. White Co has been advised that the training has been extended for the painters into a second week. White Co has also been told that during that 2nd week, both the metal and the paint supplier will be limiting their supplies to 36,000 kg of metal and 4,500 L of paint.

White Co has decided to concentrate its activities on the square and oval plates and temporarily shut down the clover leaf production line. Their customers have been informed and B Co has withdrawn its business, giving 1 weeks’ notice.

Which TWO of the following statements are true?

(1) Labour will have a shadow price of zero.

(2) The objective function will be to maximise 15 S + 15 O, where S is the number of square plates produced and O is the number of oval plates produced.

(3) If solved graphically, the optimal solution will be where the constraints for metal and paint intersect.

(4) Paint will have a positive shadow price.