Gary AJ Co. has developed a new product that has a short cycle. Information about the product is as follows.

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.

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 cost will total $130,000. These costs will apply throughout the product’s life.

The first batch will take 500 labour hours to produce. There will be a 90 percent 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.

Required:

(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.