Problem 13-12 A company manufactures hair dryers. It buys some of the components
ID: 383851 • Letter: P
Question
Problem 13-12 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? (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 4 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 _____
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? Yes___ No____
Explanation / Answer
Daily usage rate, d = 315
Daily production rate, p = 830
Annual usage or demand, D = 315*248 = 78120
Batch size, Q = 2300
a) Batches produced annually = D/Q = 78120 / 2300 = 33.97
b) 4 days later, Number of inventory = 2300 - 4 * Daily usage rate = 2300 - 4*315 = 1040
c) Average inventory = Q*(1-d/p) = (2300/2)*(1-315/830) = 714
d) No
Spare time = Lead time - Production cycle time = 2300*/315 - 2300/830 = 7.30 - 2.77 = 4.53 days
There are only 4.53 days available, but the job requires 6.5 days. So there is not enough time to do this job.