A company, which operates a 50 working weeks per year system, assembles a product at a uniform rate of 250 assemblies per week. Each assembly requires a component X in a quantity of two. The component X is manufactured in the company's own workshop and can be made either on a general purpose lathe with a production capacity of 3000 units per week or on a more sophisticated capstan lathe at a rate of 5000 units per week. The setup costs of the two lathes are $250 and $ 750 respectively. The component after manufacture is stored in special trays and storage costs per week are $6 per 1000 components. The pieces are then heated in a special oven which takes 2 weeks to complete. Because of the special settings, no other types of components can be included in the above heat treatment process, even if the oven capacity is not fully utilised. The cost of manufacture on the capstan lathe is $4.90 per unit while on the general purpose lathe the cost is $5.00 per unit. The current interest rate used by the company is 20% per year.
You are required to determine
(a) Economic Batch Quantity for the general purpose lathe and for the capstan lathe.
(b) Determine the total cost per unit for the two cases and hence recommend which machine would be used for the manufacture of the component.