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 $250$ 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.

a$.$ Approximately how many batches of heating elements are produced annually?

b$.$ If production on a batch begins when there is no inventory of heating elements on hand, how much inventory

will be on hand two days later?

c$.$ What will be the average level of inventory of the heating element, assuming each production cycle begins

when there is no inventory on hand?

d$.$ The same equipment could also be used to make a component for another of the company$$s products. That

job would require four days per cycle of the element. Setup time for making a batch of the heating elements is

a half day. Is there enough time to do this job between production of batches of heating element? Explain