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NUMBER ONE (a) Marwyck Led. produces a designer perfume called "Hint of Elegance." Production of the perfume involves the use of two ingredients, X, and X, represented by the production function given below: Y VX , X , Where Y = Number of bottles of designer perfume produced. X E Units of ingredient 1. Units of ingredient 2. Currently, the company is operating at a level where the daily usage of X, and X, is set at 250 units and 360 units respectively. The price of the designer perfume and the cost of ingredients X, and X, are random variables. The data below relate to the three random variables. Selling price of Y (per Probabilities bottle) Shs. 4,000 0.15 4,500 0.35 5,000 0.20 5,500 0.30 Cost of ingredient X, Probabilities Shs 1,000 0.10 1,500 0.05 2,000 0.35 2,500 0.50 Cost of ingredient X2 Probabilities Shs.2,000 0.25 2,500 0.15 3,000 0.40 Required: (1) Calculate the daily expected profit of the company. (5 marks) Simulate the company's profit for 10 days using the following random numbers: 58, 71, 96, 30, 24, 18, 46, 23, 34, 27, 85, 13, 99, 24, 44, 49, 18, 09, 79, 49, 74, 16, 32, 23, 02, 56, 88, 87, 59, 41, 06 (8 marks) (b) Trienen Manufacturers Led. produces component X on machine Y at a rate of 4,000 units per month. Machine Z uses component X at the rate of 1,000 units per month, the remainder being put into stock. It costs Shs. 2,000 to set up machine Y while the stock holding cost is estimated at Shs. 2.50 per unit per annum plus a 20% opportunity cost of capital per annum. Each component costs Shs. 25 to produce. Required: Compute the optimal batch size that should be produced using machine Y. (3 marks) (m1) Assume that the actual set-up cost of machine Y is Shs. 1,000 instead of Shs. 2,000. Calculate the cost of prediction error. (4 marks) (Total: 20 marks) NUMBER TWO Ditox Led. is a manufacturing company with two divisions; A and B. Division A manufactures a single standard product X, some of which is sold externally and the remainder used as an input in division B in the manufacture of product Y. The unit production costs of product K are given below: Shs. Direct material 40 Direct labour 20 Direct expense 20Variable manufacturing overheads 20 Fixed manufacturing overheads 40 Selling and packaging expenses 10 (variable) 150 Annually, 10,000 units of product X are sold externally at a price of Shs. 300 per unit and 5,000 units are transferred to division B at an internal transfer price of Shs. 290 arrive at by deducting the selling and packaging expense from the external price of Shs. 300 which is not incurred for products transferred internally. The unit production cost for product Y which uses product X as an input is given below: Shs. Cost of internally transferred products from division A to 290 division B Direct material 230 Direct labour 30 Variable overheads 120 Fixed overheads 120 Selling and packaging expenses (variable) 10 800 The manager of division B has disagreed with the basis used in arriving at the transfer price. He argues that the transfer price should be arrived at by charging the variable cost plus an agreed mark-up. He also claims that division A would not be in a position to externally sell the extra units that are transferred to division B at the price of Shs. 300. A survey on the relationship between the selling price and demand for each division was carried out by the company's Sales Director. The results are shown in the table below: Division A Selling price (Shs.) 200 300 400 Demand (units 15,000 10,000 5,000 Division B Selling price (Shs.) 800 900 1,000 Demand (units 7,200 5,000 2,800. Semi-skilled labour - 1,256 hours at a total cost of Shs. 1,281,200. The management of Swaff Marine Lid. is concerned about the cost variances and would like to learn more on the composition of the vanances. Required: Calculate the standard labour cost of the month of October 2005. (3 marks) (1) Reconcile the standard cost with the actual cost for the month of October 2005 showing the labour rate and labour efficiency variances. (5 marks) Express the labour efficiency variance in terms of labour mix and labour output variances. (Value the labour mix variances using standard rates). (8 marks) NB: The value of b in the formula for the learning curve is -0.322 for an 80% learning rate and -0.152 for a 90% learning rate. (Total: 20 marks)