Question

Wilson Manufacturing Inc. manufactures components for large vehicle and equipment assembly. One of these components is a large metal shock support bracket. The machining process involves feeding metal plates into a large milling machine, creating threaded holes, cutting to final shape and trimming to length.

• Each bracket weighs 2.5 pounds
• An average of 100,000 brackets are sold per month
• The scrap rate from this operation is 4%, mostly resulting from misalignment of the steel plate in the machining fixture
• Material costs are $600 per ton
• It takes 6 minutes of labor at a rate of $20 per hour to produce one bracket

a)     How many brackets must be produced per month to meet the sales demand?

b)     What annual savings would result from decreasing the scrap rate from 4% to 3%?

Answer 1

a) Let us assume that the number of brackets that must be produced per month to meet the sales demand = Z

Since the scrap rate is 4%, so 100 - 4 = 96% of total brackets could be used.

Sales demand per month = 100,000

Therefore,

96% of Z = 100000

0.96 x Z = 100000

Z = 100000 / 0.96 = 104166.67 = 104,167 (Rounding off)

b)

At 4% scrap rate:

Total number of brackets produced per month = 104167

Weight of one bracket = 2.5 pounds

Total weight of brackets in pounds = 104167 x 2.5 = 260417.5 pounds

Total weight of brackets in tons = 260417.5 / 2000 = 130.208 tons

Material cost per ton = $ 600

Total material cost = 600 x 130.208 = $ 78125.25

It takes 6 minutes to produce one bracket

So, the number of brackets produced in an hour = 60 / 6 = 10

Total hours required for producing 104167 brackets = 104167 / 10 = 10416.7 hours

Labour cost per hour = $ 20

So, total Labour cost = 20 x 10416.7 = $ 208334

Total cost = Total Material cost + Total Labour cost = 78125.25 + 208334 = $ 286459.25

At 3% scrap rate:

Total number of brackets produced per month = 100000 / ( 1 - 0.03) = 100000 / 0.97 = 103092.78 = 103093 (Rounding off)

Weight of one bracket = 2.5 pounds

Total weight of brackets in pounds = 103093 x 2.5 = 257732.5 pounds

Total weight of brackets in tons = 257732.5 / 2000 = 128.86 tons

Material cost per ton = $ 600

Total material cost = 600 x 128.86 = $ 77319.75

It takes 6 minutes to produce one bracket

So, the number of brackets produced in an hour = 60 / 6 = 10

Total hours required for producing 103093 brackets = 103093 / 10 = 10309.3 hours

Labour cost per hour = $ 20

So, total Labour cost = 20 x 10309.3 = $ 206186

Total cost = Total Material cost + Total Labour cost = 77319.75 + 206186 = $ 283505.75

Therefore, monthly saving from decreasing the scrap rate from 4% to 3% = 286459.25 - 283505.75 = $ 2953.5

So, Total annual saving  from decreasing the scrap rate from 4% to 3% = 12 x 2953.5 = $ 35,442