During two eighthour shifts 2000 nondefective parts are desi

During two eighthour shifts, 2000 nondefective parts are desired to produce. The standard time to complete the operation is 20 minutes, but the actual time to perform the operation takes longer and it is 30 minutes. Also it is known that oneeighth of the parts that begin fabrication are scrapped. Suppose that each of the machines used for this operation will not be available for two hours of each shift, determine the number of machines required.

Solution

Number of nondifective parts to be produced – 2000

1/8 parts gets scraped

So in order to produce 2000 non defective parts total parts to be produced will be x.

Then defective parts will be x/8

x- x/8 = 2000

8x-x/8 = 2000

X= 2285.71 (2286 parts approx)

1 part takes 30 min to complete.

The two shifts will be of 6-6 hours each as given in question.

1 machine will produce 24 parts in both shifts combine.

Total parts to be produced is 2286 parts.

Number of machines = 2286/24

= 95.25 machines required.

95.25 machines will produce 2000 non defective parts working for two 6 hours shifts with 1/8 parts get scrapped during fabrication. With average operation time of 30 minutes.