learning curves

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a) calculate the time taken for the 32nd Batch

b) calculate the selling price of the final 500 units that will allow the company to earn a total profit of 150,000 from the product

A company has developed a new product that has a short life cycle. Information about the product is as follows: Selling price and product life cycle The product will have a life cycle of 4,000 units. It is estimated that the first 3,500 units will be sold for 215 each. The product will then enter the "decline" stage of its life cycle when the selling price will be reduced. Production and costs The product will be produced in batches of 100 units. Labour will be paid at 24 per hour. Other variable costs will be 6,000 per batch. Fixed costs will total 130,000. These costs will apply throughout the product's life. Learning curve The first batch will take 500 labour hours to produce. There will be a 90% learning curve that will continue until 32 batches have been produced. Every batch produced above this level of output will take the same amount of labour time as the 32nd batch. Note: The learning index for a 90% learning curve = -0.152 The Learning Curve formula: Yx = axb Where: Yx = average time taken per batch for x number of batches a = time (or cost) for the first batch b = the learning factor x = cumulative output in batches