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 880 per day. Hair dryers are assembled daily, 249 days a year, at a rate of 330 per day. Because of the disparity between the production and usage rates, the heating elements are periodically produced in batches of 2,200 units. a. Approximately how many batches of heating elements are produced annually? (Round your answer to 2 decimal places.) Number of batches 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? Number of inventory c. What is the average inventory of elements, assuming each production cycle begins when there are none on hand? (Do not round intermediate calculations. Round your answer to the nearest whole number.) Average inventory

Explanation / Answer

a) total requirement of heating elements = days in year * hairdryers per day

= 249 * 330

= 82170

batch size = 2200

no. of batches = 82170/2200 = 37.35

b) prduction of heating element = 880

total production of heating element after 2 days = 880*2 = 1760

heating elements used in 2 days = 330*2 = 660

inventory of heating elements = 1760 - 660 = 1100

inventory of heating elements after 2 day = 1100

c)

we find the inventory level for each day starting from zero inventory to when more production required:

1st day inventory level = production - usage = 880 - 330 = 550

2nd day inventory = production - usage + inventory = 880 - 330 + 550 = 1100

3rd day inventory = production - usage + inventory = 440 - 330 + 1100 = 1210

4th day inventory = 1210 - 330 = 880

5th day inventory = 880 - 330 = 550

6th day inventory = 550 - 330 = 220

7th day again the production starts.

average inventory levels = (550+1100 + 1210 + 880 + 550 + 220)/6 = 751.67 = 752

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