Please show your work. A company\'s production facility, consisting of two ident
ID: 351332 • Letter: P
Question
Please show your work.
A company's production facility, consisting of two identical machines, currently caters only to product A. The annual demand for the product is 4000 units. Management has now decided to introduce another product, B, which uses the same facilities as that of product A. Product B has an annual demand of 2000 units. In view of the uncertainties involved in producing two products, management desires to have an overall 10 percent capacity cushion. Given the following additional information, how many more machines are required? (Assume 8 hours/shift, 2 shifts/day, 250 days/year, and that no overtime is allowed) Processing Time Setup Time per Unit (in hours) per Batch Batch Size (in hours) Product (units) 2.0 2.8 100 200 16 No additional machines are necessary. One additional machine is necessary. Two additional machines are necessary. More than two additional machines are necessary.Explanation / Answer
Time taken to meet demand of product A which is 4000 units
Cushion: 10%
Demand after including cushion: 4000*1.1: 4400
Batch size: 100 units
Processing time per unit: 2 hours
Processing time per batch: 200 hours
Setup time per batch: 8 hours
Total time per batch: 200 + 8 = 208 hours
No of batch to meet demand: 4400/100 = 44
Total time needed to meet demand of product A: 208*44 = 9152 hours
Time taken to meet demand of product B which is 2000 units
Cushion: 10%
Demand after including cushion: 2000*1.1: 2200 units
Batch size: 200 units
Processing time per unit: 2.8 hours
Processing time per batch: 560 hours
Setup time per batch: 16 hours
Total time per batch: 560 + 16 = 576 hours
No of batch to meet demand: 2200/200 = 11
Total time needed to meet demand of product A: 576*11 = 6336 hours
Total time needed to meet annual demand of product A and B: 9152 + 6336 = 15488 hours
Total time 1 machine works in 1 year: 8*2*250 = 4000 hours
So to meet the total demand company needs 4 machines which can complete work of 16000 hours which will be enough for annual demand with the required cushion