Q2 If you purchase the number of machines you calculated in Q2, and your demand
ID: 361715 • Letter: Q
Question
Q2 If you purchase the number of machines you calculated in Q2, and your demand is actually 98,500 chocolate barsfor this year, whatis your utilization? You manage a factory that makes metal products for the construction industry. Currently you have different machines for making screws, bolts, and washers. You are going to buy new machines, each of which can make all three products. The new machines can run for 7 hours per day, 225 days out of the year. Given the data below on batch sizes, setup times, and total annual demand calculate how many machines you should buy. Assume you allow a 12% cushion for the machines' capacities. Screws Bolts Washers Total Demand3,000,001,200,0001,750,000 Batch Size100,000 80,000875,000 Setup Time Per Batch2 hours 2.5hours 1.5 hours Time to Produce Each Unit 5 seconds | 8 seconds 2 secondsExplanation / Answer
Total time required to produce each item
= Total set up time + Total production time
= Set up time per batch x Number of batches + Production time/unit x Total demand
= Set up time per batch x ( Total demand/ Batch size) + Production time in hours / unit x Total demand
Therefore,
Total time required to produce screws
= 2 x 300,000/100,000 + 5/3600 x 300,000 hours
= 6 + 416.66
= 422.66 hours
Total time required to produce Bolts
= 2.5 x 1200000/80000 + 8/3600x 1200000 hours
= 37.5 + 2666.66 hours
= 2704.16 hours
Total time required to produce washers
= 1.5 x 1750000/875000 + 2/ 3600 x 1750000
= 3 + 972.22
= 975.22 hours
Total hours required to produce 3 items
= 422.66 + 2704.16 + 975.22 hours
= 4102.04 hours
Allowing for 12% cushion for machine capacities ,
Total machine hours required = 4102.04 x 1.12 = 4594.28 hours
Running capacity of a new machine per year = 7 hours/day x 225 days/ year = 1575 hours
Thus,
Number of machines to be bought
= Total machine hours required / Running capacity of a machine per year
= 4594.28/1575
= 2.917 ( 3 rounded to next higher whole number )
NUMBER OF MACHINES TO BE BOUGHT – 3
NUMBER OF MACHINES TO BE BOUGHT – 3
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