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 830 per day. Hair dryers are assembled daily, 248 days a year, at a rate of 315 per day. Because of the disparity between the production and usage rates, the heating elements are periodically produced in batches of 2,300 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 4 days later?
c. What is the average inventory of elements, assuming each production cycle begins when there are none on hand?
d. The same equipment that is used to make the heating elements could also be used to make a component for another of the firm’s products. That job would require 6 days, including setup. 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 elements?

i. Yes
ii. No

Answer 1

Answer: Please see answer below

Explanation:

a)No of batches of  heating elements produced annually =315 per day x 248 days

Batch size = 2300

No of batches  produced annually = 315 x 248 / 2300 = 33.96  = 33.97  batches

b)

Number  of inventory daily during  production  

= Daily production rate – Daily usage rate

= 830 – 315

= 515

so number of inventory on hand 4 days later = 515 per day x 4 days = 2060

c) Inventory for the  heating elements = Batch size x ( 1 – daily requirement/ Daily production ) = 2300 x ( 1 – 315/830 ) = 2300 x ( 1 – 0.38) = 1,426

our minimum inventory per day =0

Average inventory = ( Max. inventory + Min inventory )/ 2 = 1426/2 = 713

d)we already have that  33.97batches of production of heating elements are required .

set up time of heating element per batch to use = 1/2 day

then Total set up time required in a year = 0.5 x 33.97days = 16.985 days

Number of heating elements required in a year = 315 per day x 248 days = 78,120

At production rate of 830 per day ,with no set up time required for heating element = 78120 /830 = 94.12 days

the total time required in a year for heating elements  will now be

= Actual production time + Set up time

= 94.12 + 16.985

= 111.105 days

which means the spare time available annually to produce other components = 248 days  – 111.105 = 136.895= 136.9 days

i )YES, since the time required to complete the other job is 6 days , there would be enough time because 6 days is less than 136.9 days of spare time