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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 inventory

Explanation / 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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