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4 June, 22:44

During one eight-hour shift, 750 non-defective parts are desired from a fabrication operation. The standard time for the operation is 15 minutes. Because the machine operators are unskilled, the actual time it takes to perform the operation is 20 minutes, and, on average, one-fifth of the parts that begin fabrication are scrapped. Assuming that each of the machines used for this operation will not be available for one hour of each shift, determine the number of machines required.

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  1. 4 June, 23:38
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    No. of Machines Required = 47

    Explanation:

    First, we calculate the number of parts that can be manufactured by one machine during the shift. For that purpose, we use following formula:

    No. of Parts Manufactured by 1 Machine = Total Operating Time/Time taken to perform Operation

    where,

    Total Operating Time = 8 h - 1 h = (7 h) (60 min/h) = 420 min

    Time taken to perform operation = 20 min

    Therefore,

    No. of Parts Manufactured by 1 Machine = 420 min/20 min

    No. of Parts Manufactured by 1 Machine = 21

    Now, we will calculate the no. of non-defective parts manufactured by 1 machine. Since, it is given that one-fifth of the parts manufactured by machine are defective. Therefore, the non-defective parts will be: 1 - 1/5 = 4/5 (four-fifth).

    No. of Non - Defective Parts Manufactured by 1 Machine = N = (4/5) (21)

    N = 16.8 = 16 (Since, the 17th part will not be able to complete in time)

    So, the no. of machines required to produce 750 non-defective parts is given by:

    No. of Machines Required = No. of non-defective parts required/N

    No. of Machines Required = 750/16

    No. of Machines Required = 46.9

    No. of Machines Required = 47 (Since, 46 machines will not be able complete the job)
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