Question

A metal part for which annual demand is 180,000 units is made on a CNC machine at a rate of 270 parts per hour. It can be made using tool steel costing $0.30 per pound or using brass stock costing $1.40 per pound. The weight per steel piece is 0.0353 pounds and the weight per brass piece is 0.0384 pounds. When it is made using steel, it was found that 50% of the parts made per hour are defect-free; when it made using brass stock, it was found that 85% of the parts made per hour are defect-free. If the total labor and overhead cost for operating the machine is $25.00 per hour, how much more does it cost to make 1000 defect-free parts from steel than to make 1000 defect-free parts from brass on this machine?

Answer 1

To create 1000 defect free parts from steel we need to manufacture 1000/50% = 1000/0.5 = 2000 parts in total (as 50% is defect free)

To manufacture 2000 parts from steel we will need 2000/270 = 7.407 hours

So, Cost of labor & overhead for 7.407 hours = 7.407 * 25 = $185.185

Total weight Requirement for 2000 steel parts = 0.0353 * 2000 = 70.6 pounds

Total cost of Steel = 70.6 * 0.30 = $21

Hence Total cost of manufacturing from Steel= 185.185 + 21 = $206.185

similarly, To create 1000 defect free parts from brass we need to manufacture 1000/85% = 1000/0.85 = 1176.47 or 1177 parts in total (as only 85% are defect free)

To manufacture 1177 parts from brass we will need 1177/270 = 4.359 hours

So, Cost of labor & overhead for 4.359 hours = 4.359 * 25 = $108.98

Total weight Requirement for 1177 brass parts = 0.0384 * 1177 = 45.2 pounds

Total cost of Brass = 45.2 * 1.4 = $63.28

Hence Total cost of manufacturing from Brass= 108.98+63.28 = $172.26

Hence Total Extra Cost to manufacture from Steel = 206.185- 172.26 = $33.92

Hence answer is 33.92