1.Mechanics Ltd makes two products, A and B. Any quantities produced can be sold for 120 per unit of product A and 50 per unit of product B. Variable costs for the two products are as follows:

Product A Product B

Materials (at 10 per kg) 30 10

Labour (at 12 per hour) 48 6

Other variable costs 12 10

Total 90 26

Next month, only 8,400 kg of material and 6,000 labour hours will be available. Mechanics Ltd aims to maximise its profits each month and wants to use the linear programming model to establish an optimum production plan.

Required:

If X is the number of units of Product A made and sold, and Y is the number of units of Product B, demonstrate the objective function and constraint statements (relating to material and labour).

2.Helena Ltd specialises in the production of a wide range of kitchen equipment. The company is about to launch a new model of washing machine (HL-16). The technology used in HL-16 is unique so Helena Ltd has patented it so that no competitors can enter the market for three years. The company is now trying to ascertain the best pricing policy that they should adopt for the HL-16 launch onto the market.

The costs of producing each unit of washing machine HL-16 is as follows:

Direct materials337

Direct labour198 (11 hours at 18)

Fixed overheads 17

Total cost 552

The management accountant has produced the following information:

If the company set the price at 955, only, 2,000 units would be demanded per annum. Demand is very responsive to price changes and research has established that, for every 60 increase in price, demand would be expected to fall by 2,000 units.

Required:

Calculate the sales price and output quantity that maximise the annual profit for the product.

3.Global Fox plc, a computer manufacturing company, is considering investing in a four-year investment project. The company has already spent 5 million on research, but this project will require the purchase of equipment costing 800,000 with the expected life of four years.

The company's policy is to depreciate fixed assets on the straight-line basis over their estimated useful economic lives. It is expected that that the new equipment will be disposed of for estimated proceeds of 120,000 at the end of the life of the project.

The profit before interest and tax from the project is expected to be 170,000 in Year 1 and then to increase at the rate of 4% per annum for the remainder of the project life.

Global Fox plc has sufficient taxable profits from other parts of its business to enable the offset of any pre-tax losses on this project. The after-tax cost of capital of 14% is used to evaluate projects of this type.

The taxation information is as follows:

Taxation rate: 30% one year in arrears

Tax depreciation: 25% per annum of the reducing balance, with a balancing adjustment in the year of disposal. The first claim for an allowance would be made against Year 1 profits.

It is anticipated that 30,000 per year will be spent at the end of year 2 on maintenance and 40,000 per year will be paid at the beginning of years 3 and 4 on major technical improvements. The initial outlay would be paid at the start of the project and remaining cash flows can be assumed to occur at the end of the relevant year.

Required:

(i)Calculate the Net Present Value (NPV) of the project. You should round your figures to the nearest .

(ii)Recommend whether Global Fox plc should go ahead with the investment project.

(iii)Measure the sensitivity of the project to changes in initial investment.

(iv)Compare and contrast the terms 'hard' and 'soft' capital rationing.

4.You are the Management Accountant of Nic Ltd that manufactures and sells optical equipment using the same direct labour work force on all the products. There is a high demand for their products but sometimes the company operates under the constraint of a shortage of labour or materials.

The directors of the company want to increase production by ensuring that it uses the limited resources available to maximise profits by selling the optimum mix of the products. The production team is currently formulating a production plan for the company's two principal products, A and B, and wishes to determine the optimal product mix.

Nic Ltd sold 10,000 units of Product A and 20,000 units of Product B last month (July). The budgeted sales based on the customer demand for the next month (August) are estimated to be 15% more than the last month's sales. The following information per unit is available for these two products:

AB

Selling price45.0050.00

Material X (@5.00 per kg)7.5015.00

Material Y (@2.00 per kg)10.00 6.00

Direct labour (@10.00 per hour)2.501.50

Absorbed overhead (@6.00 per hour)1.500.90

For August, availability of materials and direct labour to the company is as follows: 70,000 kg of material X, 190,000 kg of material Y and 8,000 hours of direct labour. Nic Ltd does not keep any stock of materials, work-in-progress or finished goods.

(i) Prepare calculations to determine the limitations that will prevent Nic Ltd from fulfilling all of the customer demand for August.

(ii) Calculate the optimal production plan for August that would maximise the company's profit (rounding to two decimals). Your answer should also include the calculation of the total contribution based on your optimal plan for August.

5.Berta Ltd makes specialist machinery to customers' specifications. Recently, just as Berta Ltd completed a particular machine for a customer, it received information that the customer had gone bankrupt with no possibility of any payment to Berta Ltd being seen as likely.

The total contract price was 55,000. The contract specified that payment must be made in stages, as the machine's manufacture progressed. Berta Ltd had received 30,000 in progress payments for the machine. It is estimated that the machine could be sold, as it stands, for 40,000.Another potential customer has been identified for the machine, but this would require alterations to it. Details of the alterations are as follows:

Material A. The required quantity is held in inventories. This cost 3,000 when it was bought. It would cost 3,200 to replace it. The material is hazardous and would cost the business 500 to scrap it. Berta Ltd uses it constantly.

Material B. By coincidence the appropriate quantity of this material was ordered recently for another contract that was subsequently abandoned because the material was not delivered in time. Berta Ltd does not normally use this material and its scrap value is 2,000. The original cost price was agreed at 5,000. Though the contract to buy this material is binding, the supplier will accept 4,000 to compensate for the late delivery. The current market buying price is now 3,500.

Material C. 25 units of this material will be required. This is in general use in the company. An order for 30 units is shortly to be placed for another job. The price for this material is 65 a unit, but the supplier allows a bulk discount of 5 a unit, for the entire order, for orders of 50 units and above.

Labour. 50 hours of labour will be required for the alterations. Labour is a fixed cost to Berta Ltd, because members of staff are paid in full the normal 13 an hour whether there is work for them to do or not. 20 hours, of the required 50 hours, can be provided by members of staff who currently have no work to do. Only taking staff off other work can provide the remaining 30 hours. This other work is charged out to customers at 25 an hour.

Required:

Calculate the minimum price that Berta Ltd could charge the customer for the altered machine, such that the shareholders would be no worse off as a result. In your answer, you must make detailed notes showing how each cost has been arrived at and clearly explain why each of the costs above has been included or excluded from the calculation.