Monthly usage rate for a certain part is $15,000$ units. The part is produced in batches and its manufacturing costs are estimated to be $$7\mathrm{.}40.$ Holding cost is $20\%$ of piece cost. Currently the production equipment used to produce this part is also used to produce $19$ other parts with similar usage and cost data $($assume the data to be identical for purposes of this problem$).$ Changeover time between batches of the different parts is now $4\mathrm{.}0$ hours, and cost of downtime on the equipment is $$275/$hr$.$ Determine the economic batch size for the part in question. Units are $"$pc$"$ and the answer should be an integer.