A company is about to begin production of a new product. The manager of the department that will produce one of the components for the product wants to know how often his machine will be available for other work. The machine will produce the item at a rate of 200 units a day. 80 units will be used daily in assembling the final product.

The company operates five days a week, 50 weeks a year. The manager estimates that it will take almost a full day to get the machine ready for a production run, at a cost of $300. Inventory holding costs will be $10 per unit per year.

a) What production run quantity should be used to minimize total annual setup and holding costs?

b) What is the length of a production run in days?

c) During production, at what rate will inventory build up?

d) If the manager wants to run another job between runs of this item, and needs a minimum of 10days per cycle of this job for the other work, will there be enough time?