A company manufactures hair dryers. It buys some of the components, but it makes

Question

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 853 per day. Hair dryers are assembled daily, 249 days a year, at a rate of 320 per day. Because of the disparity between the production and usage rates, the heating elements are periodically produced in batches of 2,133 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 four days later?

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

Explanation / Answer

Heating element production per day (H)=853

Dryer production per day(D)=320

Workiing days=249

Annual production of hair dryers=320*249=79680

Per batch production of heating elements=2133

a)number of batches of heating element produced annually=79680/2133=37.35 batches/yr

b)Production of heating elements in four days=4*853=3412

Production of dryers in 4 days=4*320=1280

hence inventory=3412-1280=2132

c) Max Inventory=Batch production*(H-D)/D=2133*(853-320)/853=1332.8

hence avg inventory=1332.8/2=666.4=667

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