As you already know, Charlie Cooker keeps meticulous records and knows that the overall daily demand for the C$4$ Chocolate Chip Crunch Cookie is $1500$ dozen. The production line runs from $9$am to $4$pm daily Monday through Saturday. C$4$ has very high freshness and quality standards, so they only sell cookies made on the same day. The owner, Charlie Cooker, knows that he can sell more cookies if he can just make them.

He has identified the bottleneck to be the extruding machine and he wants to analyze the impact of using four managerial levers he has at his disposal to increase the capacity of the extruder and therefore increase the daily production of C$4$ Chocolate Chip Crunch Cookies. The lever you want to analyze here is adding cutters to the extrusion machine.

Adding cutters is more complex than you may think on the surface. Although adding cutters adds to the processing capacity of the machine, if setup time is not reduced, it also adds to non$-$value added time because it takes longer for each setup when more cutters have to be cleaned before processing a batch. If the setup time were zero or if adding a cutter did not increase setup time, then adding cutters would always result in a net increase in daily capacity. However, cleaning time is too long then adding cutters could actually decrease daily capacity because it would increase setup time and result in fewer batches produced in a day. As you can imagine this can be a complex situation in that what may look like a good way to increase capacity $($adding cutters$)$ may backfire if setup time cannot be reduced. Adding cutters also involves a capital expense for the new equipment and installation, so we want to be good stewards and use resources wisely.

The good news is that most setup times can be greatly reduced. In The Toyota Way, levelling out the workload in the lawnmower engine plant example is only made possible by drastically reduced setup times. Consider this excerpt from page $97.$

"Though dramatically reducing setup time in most plants may seem unrealistic at first, Toyota did exactly that in the $1960$s$.$ Shigeo Shingo, an industrial engineer...helped the company achieve an average changeover time reduction of over $97$ percent."

That makes me say, "Wow!" Imagine taking a $97\%$ savings in a process step that happens thousands of times per year. This illustrates that reducing setup times beyond what is assumed possible IS possible in most cases, as exemplified by Toyota. Therefore, when we consider adding cutters to the extrusion machine, we must simultaneously consider how to reduce setup time.

We start with an extruder setup for this problem of $3$ cutters working at a rate of $26$ cookies per minute per cutter. The time it takes to load each batch of dough is $30$ seconds. The time to clean each cutter head is $30$ seconds, and the cutters can only be cleaned one at a time so it takes $120$ seconds to clean all three. If we were to add a fourth cutter to this machine under these parameters, the total daily capacity would $($counterintuitively$)$ decrease! This is because the $30$ second cleaning time adds to the setup time in such as way that the additional output of the added cutter is subsumed by fewer batches being produced in a shift. Fewer batches are produced because more of the available time is being spent on setup $($non$-$value added$).$ Although the extrusion machine can accommodate expansion of up to six total cutters, we need to understand the system dynamics. Before adding a fourth, fifth, or sixth cutter, we need to determine how much cleaning time must be reduced for the additional cutter$($s$)$ to add value by increasing overall daily production.

Given a starting batch size of $8$ pounds of dough, the standard cookie size of $2$ ounces, and the current shift length of $7$ hours, Charlie Cooker is considering adding $2$ more cutter$($s$)$ to the extrusion machine. find the number of seconds you'll need to DECREASE individual cutter cleaning time from the current time of $30$ seconds for the added cutter$($s$)$ to increase daily capacity from the base setup in this problem. You can only adjust cleaning time in one$-$second increments.

If the 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.

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