A company manufactures two different products: Alpha and Beta. Each of this prod
ID: 344948 • Letter: A
Question
A company manufactures two different products: Alpha and Beta. Each of this product must be processed by machine K. The company has several identical machines K. The company uses a 12 percent capacity cushion. The unit processing time (minutes per unit), lot size (units per lot), and the setup time (hors per lot are shown below Product Alpha; 31 minutes per unit; 90 units per lot; 3.7 hours per lot Product Beta; 26 minutes per unit; 120 units per lot; 5.2 hours per lot; The company operates two 8-hour shifts per day, 242 days per year How many machines are required to meet the yearly demand of 31050 units of Alpha and 30720 units of Beta? Use at least 4 decimals in your calculation and answer Do not use any comma in your answer You must show your calculation steps on your spreadsheet The required total setup time is hours per year The required number of machines K is F9 F10 FI F12 F8 0Explanation / Answer
Total amount of time in a year required to produce a certain quantity of a particular item ( in hours )
= Number of lots x Set up time in Hours per lot + Processing time / unit x Yearly demand ( units)
= ( Yearly demand/Lot size ) x Hours per lot + Processing time in hour / unit x Yearly demand ( units )
Therefore ,
Total amount of time in hours required for Alpha in a year
= ( 31050 / 90 ) x 3.7 + ( 31/60) x 31050
= 1276.5 + 16042.50
= 17319 hours
Required set up time = 1276.5 hours
Total amount of time required for Beta in a year
= ( 30720/120 ) x 5.2 + ( 26/60 ) x 30720
= 1331.20 + 13312
= 14643.20 hours
Required set up time = 1331.20 hours
Total required set up time = 1276.5 hours + 1331.20 hours = 2607.70 hours
REQUIRED TOTAL SET UP TIME IS 2607.70 HOURS PER YEAR
Amount of time available for operation in a year = 2 shifts x 8 hours/ shift x 242 days = 3872 hours
Total amount of operation time required for producing alpha and beta
= 17319 + 14643.20 hours
= 31962.20 hours
The required number of machines K = 31962.20 / 3872 = 8.2547
THE REQUIRED NUMBER OF MACHINES K = 8.2547
REQUIRED TOTAL SET UP TIME IS 2607.70 HOURS PER YEAR
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