Acme is exploring two locations for a new plant to supply product for a government contract. They ...

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?