Question

Determine the labor costs required to manufacture the 100^th item if the first item requires 50 days to produce and the learning curve is 82%. The manufacturing process requires two 9-hour shifts working each day, with 8 employees per shift. The employees are paid $17.50 per hour.

Answer 1

Solution :-

As per Learning Curve theory

Y = ax^b

Where a is time required for 1st unit = 50 * 9 * 2 = 900

X is Number of Units Produced

b is learning coefficient

Value of b = Log ( 0.82 ) / Log ( 2 ) = - 0.086186 / 0.30103 = - 0.2863

Now Cummulative hours required for 99 Units =

Y = ( 900 ) ( 99 )^-0.2863

Y = 900 * 0.268318 = 241.486 hours

Therefore time required for 99 Units = 99 * 241.486 = 23907.114 Hours

Now Cummulative hours required for 100 Units =

Y = ( 900 ) (100 )^-0.2863

Y = 900 * 0.267547 = 240.792 hours

Therefore time required for 100Units =100 * 240.792 = 24079.225 hours

Therefore time Required for 100 th Units = 24079.225 hours - 23907.114 Hours = 172.11 hours

Labor cost for 1 hour per employee = $17.50

Now Labor Cost for one unit that is of 8 workers per unit for 172.11 hours = 172.11 * 17.50 * 8 = $24,095.54

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