We know that a process is only as fast as its bottleneck. This means the speed or capacity of a bottleneck in a process really determines the overall output or capacity of the process. Charlie Cooker knows that his extruder is the bottleneck for the cookie shop, so to find the daily capacity of the shop, he simply needs to find the daily capacity of the extruder. The process is a batch process, meaning the product moves from step to step in batches, where batch size is determined by the weight of dough. Each batch must be completed by the extruder before a new batch can be started at the extruder. The time it takes for the extruder to complete one batch $($total batch time$)$ is made up of the sum of the setup time $($which is non$-$value added because it does not do anything to transform the dough into a finished product$)$ and the processing time. The setup time in this step is the total of the time taken to load the dough into the machine and to clean all the cutters. The processing time for a batch is the total time to extrude all the cookies in the batch after the dough has been loaded and the cutters have been cleaned. Since the process works only on batches, we want to avoid starting any batch that would cause the process to work beyond the normal shift length. To determine daily capacity here, we first need to determine how many whole batches can be completed in one shift. By dividing the shift length by the time it takes to complete one batch $($total batch time$),$ we can determine how many batches can be completed in one day. Since we are interested in only whole batches, this calculation will always be rounded down. Once the number of batches produced in a shift has been determined, then the total capacity can be found by multiplying the number of cookies in a batch by the number of batches produced.

The extruder setup for this problem is $3$ cutters working at a rate of $19$ cookies per minute per cutter. It takes $30$ seconds to load each batch of dough and an additional $34$ seconds to clean each one of the cutters.

Given a batch size of $11$ pounds of dough, the standard cookie size of $2$ ounces, a shift length of $9$ hours, find the capacity of the process in cookies per day. This will be a whole number.

If batch size results in a fractional number of cookies per batch, round down to the number of completed cookies in the batch. For example a batch size of $8\mathrm{.}6$ pounds will result in $68\mathrm{.}8$ cookies per batch, but we only want completed cookies so we would round down to a batch size of $68.$ You should only use whole batches completed per shift in your daily capacity calculation. For example, if you calculate that $145\mathrm{.}7$ batches can be completed in a shift, round down to $145$ whole batches.

Enter your answer below using only numerical characters $($i$.$e$.,$ no commas$).$