A company manufactures hair dryers. It buys some of the components, but it makes
ID: 347857 • Letter: A
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 810 per day. Hair dryers are assembled daily, 246 days a year, at a rate of 305 per day. Because of the disparity between the production and usage rates, the heating elements are periodically produced in batches of 2,100 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 3 days ater? 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 inventoryExplanation / Answer
To be calculated:
(a) Number of batches of heating elements produced annually
(b) On-hand inventory 3 days later
(c) Average inventory of elements
Given values:
Production rate of heating element = 810 per day
Assembling rate of hair dryers = 305 per day
Number of working days in a year = 246 days
Number of hair dryers assembled annually = 305 x 246 = 75,030
The number of heating elements will be equal to the number of hair dryers assembled annually because one hair dryer will consist of one heating element. Therefore,
Number of heating elements produced annually = 75,030
Batch size of heating elements = 2100 units
Solution:
(a) The number of batches of heating elements produced annually is calculated as;
Number of batches = Total number of heating elements / Batch size of heating elements
Number of batches = 75030 / 2100
Number of batches = 35.73 batches
(b) If production on a batch begins when there is no inventory of heating elements on hand, the on-hand inventory 3 days later will be calculated as;
On-hand inventory after 3 days = 3 x (Production rate of heating element - Assembling rate of hair dryers)
On-hand inventory after 3 days = 3 x (810 - 305) = 3 x (505) = 1,515
On-hand inventory after 3 days = 1,515 units
(c) Average inventory of elements is calculated as;
Average inventory = 1/2 x [Q x (1 - d/p)]
where, Q = Batch size or EPQ (Economic production quantity)
d = demand
p = production rate
Average inventory = 1/2 x [Q x (1 - d/p)]
Average inventory = 1/2 x [2100 x (1 - 305/810)]
Average inventory = 1/2 x [2100 x (1 - 0.38)]
Average inventory = 1/2 x [2100 x (0.62)]
Average inventory = 1/2 x 1302
Average inventory = 651 units
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