Acme is exploring two locations for a new plant to supply product for a government contract. They dispatch a team of industrial engineers and cost estimators to the Minneapolis-St

Paul area of Minnesota and to Kennewick-Pasco-Richland area in Washington. After conducting some tests, the teams return with some unusual findings, the Minneapolis-St. Paul workers seem to obey classic learning effect rules; their learning rate is 80% and is based on a doubling of output. They are much slower than their counterparts at the other site; it is estimated that the first batch units they assemble will take them 700 hours. The workforce in the Kennewick-Pasco-Richland area is much faster; their first batch will take only 470 hours. Strangely, these workers also exhibit learning effects, but their learning is based on a tripling of output rather than the traditional doubling and their rate is 78%. How many batches must be made before Minneapolis-St. Paul's time falls below Kennewick-Pasco-Richland's?

The crossover point is just above the 64th unit; at the 64th unit the Kennewick-Pasco-Richland workers are faster by one hundredth of an hour and at the 65th unit the Minneapolis-St. Paul workers are faster by a quarter of an hour.

Yx = Minneapolis-St. Paul
Yx = Kennewick-Pasco-Richland
Yx = =
=
700X-.32193 = 470X-.22616

=
1.489362 = X-.095769
1n(1.489362 ) = 1n(X-.095769 )
0.398349 = 0.095769 1n(X)
= 1n(X)

exp = X

X = 64.03765