A metal part for which annual demand is 220,000 units is made on a CNC machine a

Question

A metal part for which annual demand is 220,000 units is made on a CNC machine at a rate of 330 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? (Enter your answer as a number without the dollar sign.)

Explanation / Answer

for 1000 defect free parts made up of steel we need to make (1000/0.5 = 2000) parts since 50% are defect free.

similarly for 1000 defect free parts of brass we need to make (1000/0.85 = 1176.5 approx 1177 parts.

rate of production = 330parts per hr

therefore time taken to make 2000 steel parts = 2000/330=6.06 hrs

labour cost for making steel parts = 25*6.06 =151.5

time take to make 1167 parts of brass =1167/330 = 3.53 hrs

labour cost for making brass parts = 25*3.53 =88.25

steel required for 2000 parts = 0.353 *2000 = 706 pounds

cost of steel = 0.3*706 = 211.8

brass required for 1167 parts = 1167 *0.0384 = 44.81 pounds

cost of brass = 44.81* 1.4 = 62.73

therefore the extra mone to make 1000 defect-free parts from steel than to make 1000 defect-free parts from brass on this machine = total cost for making steel parts - total cost for making brass parts

                  = (151.5+211.8)-(88.25+62.73) =212.32

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