Accounting in Management - Assignment Example

PART-A Optimum Production ment Particulars Alpha Beta Delta Selling price (Per Unit) £ 55 £ 44 £ 49 Less Marginal/Variable cost: Direct Materials £ 30 £ 12 £ 12 Direct Labour £ 10 £ 10 £ 20 Total £ 40 £ 22 £ 32 Contribution (Per Unit) £ 15 £ 22 £ 17 Considering the limiting factors that there are 1500 labour hours at £ 20 per hour and 10000 Kg of materials at £ 3 per Kg, the optimum production schedule for maximisation of the profit will be as follows: - Section 1 Production Mixes Alpha Beta Delta 500 units of Alpha at the rate of £ 55 £ 27500 500 units of Beta at the rate of £ 44 £ 22000 750 units of Delta at the rate of £ 49 £ 36750 Marginal Costs (Alpha) Direct Material 500 x 30 = 15000 Direct Labour 500 x 10 = 5000 £ 20000 Marginal Costs (Beta) Direct Material 500 x 12 = 6000 Direct Labour 500 x 10 = 5000 £ 11000 Marginal Costs (Delta) Direct Material 750 x 12 = 9000 Direct Labour 750 x 20 = 15000 £ 24000 Contribution (Total) £ 7500 £ 11000 £ 12750 The interpretation of the results obtained through the calculations in Section 1 is as below: - A careful scrutiny of the data provided reveals that the contribution of Beta at £ 22 is the highest. Since the main goal of Portland Ltd is profit maximisation, and there are limiting factors that labour hours and materials are restricted to 1500 labour hours at the rate of £ 20 per hour and Materials 10,000 Kg at £ 3 per Kg respectively, we will first and foremost complete the full production of Beta that is 500 units. This production would entail the use of 250 labour hours and 2000 Kgs of Materials. Thus, after the demand of Beta is met, we have a balance of 1250 Labour hours and 8000 Kg of Materials. The next higher contributor is Delta. Therefore, we would produce the full order of Delta for this 750 Labour hours and 3000 Kg of Materials. The balance left over would be 500 Labour hours and 5000 Kg of Materials, which would be used for production in respect of Alpha which is the least contributing product. The limiting factors only allow production of 500 Units of Alpha. The statement shown below would explain the position. Particulars Alpha Beta Delta Total Labour hours 500 250 750 1500 Material (Kg) 5000 2000 3000 10000 The above production of 500 units of Alpha, 500 units of Beta, and 750 units of Delta, constitutes the best product mix under the given circumstances, yielding the total contribution of £ 31250. The alternative product mixes are given below: - Production mixes Alpha Beta Delta 500 units of Alpha at the rate of £ 55 £ 27500 500 units of Beta at the rate of £ 44 £ 22000 750 units of Delta at the rate of £ 49 £ 36750 Marginal Costs (Alpha) Direct Material 500x 30 = 15000 Direct Labour 500x 10 = 5000 £ 20000 Marginal Costs (Beta) Direct Material 500 x 12 = 6000 Direct Labour 500 x 10 = 5000 £ 11000 Marginal Costs (Delta) Direct Material 750 x 12 = 9000 Direct Labour 750 x 20 = 15000 £ 24000 Contribution (Total) £ 7500 £ 11000 £ 12750 600 units of Alpha at the rate of £ 55 £ 33000 500 units of Beta at the rate of £ 44 £ 22000 500 units of Delta at the rate of £ 49 £ 24500 Marginal Costs (Alpha) Direct Material 600x 30 = 18000 Direct Labour 600 x 10 = 6000 £ 24000 Marginal Costs (Beta) Direct Material 500 x 12 = 6000 Direct Labour 500 x 10 = 5000 £ 11000 Marginal Costs (Delta) Direct Material 500 x 12 = 6000 Direct Labour 500 x 20 = 10000 £ 16000 Contribution (Total) £ 9000 £ 11000 £ 8500 750units of Alpha at the rate of £ 55 £ 41250 500 units of Beta at the rate of £ 44 £ 22000 125 units of Delta at the rate of £ 49 £ 6125 Marginal Costs (Alpha) Direct Material 750x 30 = 22500 Direct Labour 750 x 10 = 7500 £ 30000 Marginal Costs (Beta) Direct Material 500 x 12 = 6000 Direct Labour 500 x 10 = 5000 Marginal Costs (Delta) Direct Material 125 x 12 = 1500 Direct Labour 125 x 20 = 2500 £ 11000 £ 4000 Contribution (Total) £ 11250 £ 11000 £ 2125 Comparative study of the various alternative production mixes. Product mixes Relevant Contribution 500 Units of Alpha £ 7500 500 Units of Beta £ 11000 750 Units of Delta £ 12750 Total £ 31250 600 Units of Alpha £ 9000 500 Units of Beta £ 11000 500 Units of Delta £ 8500 Total £ 28500 750 Units of Alpha £ 11250 500 Units of Beta £ 11000 125 Units of Delta £ 2125 Total £ 24375 It seen from the above comparative study that Alternatives 2 and 3 yield lower contributions as compared to Alternative 1. Therefore, Alternative 1 is the most appropriate. The method adopted in Section 1 is Marginal Costing to determine the maximum profit for Portland Ltd, taking in to consideration the limiting factor, viz.1500 labour hours and 10000 Kgs. Materials Linear Programming: In this analysis there are three types of products Alpha, Beta, Delta. The number of items produced is 500 Units of Alpha, 500 Units of Beta, and 750 Units of Delta respectively. Total contribution is£ 7500 Alpha, £ 11000 Beta, and £ 12750 Delta. There are two constraints in this scene. Materials available are only 10000 Kg and labour hours 1500. Alpha, Beta, Delta denoted as X1, X2, X3. Objective Z = 7500X1 + 11000X2 + 12750X3 Subject to constraints 5000X1 + 2000X2 + 3000X3= 10000 250X1 + 250X2 + 750X3 = 1500 X1 > 0, X2 >0 and X3>0 The limiting factors in the problem are availability of 1500 labour hours @ £ 20/hour and 10,000kgs of materials @ £ 3/kg. Since 1000 units of Alpha would consume 10,000Kgs materials, there would be no materials left for producing Beta and Delta. Beta has the maximum contribution of £ 22/unit and therefore it has to be produced on first Priority. The next higher contribution is from Delta viz. £ 17/unit. Therefore, the second priority would be given to Delta and third priority to Alpha. This is also in line with Principles of Marginal Costing and meets the requirements of Portland Ltd, of maximize their profit. The circumstances in which we would use the two alternatives are: First Alternative: Product Mix: 600 units of Alpha, 500units of Beta and 500units of Delta. The contribution/unit are £ 15, £ 22, and £ 17 for Alpha, Beta and Delta respectively. Next we multiply unit contribution with ordered quantity for each product. Objective: Z =9000 X1 + 11000 X2 + 8500 X3 Subject to constraint For producing 600 units of Alpha, 6000 kg of materials are required For producing 500 units of Beta, 2000 kg of materials are required For producing 500 units of Delta, 2000 kg of materials are required. For producing 600 units of Alpha, 300 labour hours are required For producing 500 units of Beta, 250 labour hours are required. For producing 500 units of Delta, 500 labour hours are required 6000 X1 + 2000X2 + 2000X3 Read More