Problem:

A company manufactures hair dryers. It buys some of the components, but it makes the heating element, which it can produce at the rate of 800 per day. Hair dryers are assembled daily, 250 days a year, at a rate of 300 per day. Because of the disparity between the production and usage rates, the heating elements are periodically produced in batches of 2,000 units.

Required:

Question 1) Approximately how many batches of heating elements are produced annually?

Question 2) If production on a batch begins when there is no inventory of heating elements on hand, how much inventory will be on hand three days later?

Question 3) What is the average inventory of elements, assuming each production cycle begins when there are none on hand?

Solve the given numerical problem and illustrate step by step calculation.