12 A tire plant must produce an average of 100 tires per day. The plant produces tires in a batch of size x. The plant manager must determine the batch size x that minimizes the time a batch spends in the plant. From the time a batch of tires arrives, it takes an average of 2 1 0 of a day to set up the plant for production of tires. Once the plant is set up, it takes an average of 1 1 50 day to produce each tire. Assume that the time to produce a batch of tires is exponentially distributed and that the time for a batch of tires to “arrive”
is also exponentially distributed. Determine the batch size that minimizes the expected time a batch spends in the plant (from arrival of batch to time production of batch is completed).