A company needs to fabricate 128 widgets and wants to estimate how long it will

Question

A company needs to fabricate 128 widgets and wants to estimate how long it will take. The nature of making these types of widgets makes them susceptible to learning curve effects The company has data from two previous projects to use for comparison. On one project it took 30,000 hours to make 64 similar widgets, and on another project it took 65,910 hours to make 512 widgets How many hours will it take to fabricate the 128 widgets. You may assume that the widgets in each project will be similar enough that it will take the same amount of time to make the first widget in each project, and that the rate of learning will be the same in each project. Answer to the nearest hour ?? How many hours will it take to make the last widget (ie widget number 128). Answer to the nearest hour

Explanation / Answer

Cumulative average time learning curve will apply. Let 'r' be the learning curve %.

Cumulative average time for 64 parts = 30000/64 = 468.75 hours
Cumulative average time for 512 parts = 65910/512 = 128.73 hour

Since 64 x 23 = 512,
So, 468.75 x r3 = 128.73
or, r3 = 0.2746
or, r = 0.65 i.e. 65%

So, Cumulative average time for 128 parts = 468.75 x r1 = 468.75 x 0.65 = 304.688 hours.

So, the total time to fabricate 128 widgets = 304.688 x 128 = 39,000 hours

The cumulative average time for 128 parts = Time for the first part x 128log(r) / log(2)
or, 304.688 = Time for the first part x 128-0.6215
or, Time for the first part = 6215.286 hours

So, The cumulative average time for 127 parts = 6215.286 x 127-0.6215? = 306.17 hours

So, the total time to fabricate 128 widgets = 306.17 x 127 = 38884.39 hours

So, time to fabricate the 128th part = 39,000 - 38884.39 = 116 hours

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