# Math

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You and your roommate have timed the necessary physical operations. The ﬁrst physical production step is to wash out the mixing bowl from the previous batch, add all of the ingredients, and mix them in your food processor. The mixing bowls hold ingredients for up to three dozen cookies. You then dish up the cookies, one dozen at a time, onto a cookie tray. These activities take six minutes for the washing and mixing steps, regardless of how many cookies are being made in the batch. That is, to mix enough dough and ingredients for three dozen cookies takes the same six minutes as one dozen cookies. However, dishing up the cookies onto the tray takes two minutes per tray. The next step, performed by your roommate, is to put the cookies in the oven and set the thermostat and timer, which takes about one minute. The cookies bake for the next 9 minutes. So total baking time is 10 minutes, during the ﬁrst minute of which your roommate is busy setting the oven. Because the oven only holds one tray, a second dozen takes an additional 10 minutes to bake.
Your roommate also performs the last steps of the process by ﬁrst removing the cookies from the oven and putting them aside to cool for ﬁve minutes, then carefully packing them in a box and accepting payment. Removing the cookies from the oven takes only a negligible amount of time, but it must be done promptly. It takes two minutes to pack each dozen and about one minute to accept payment for the order.

A. What is the bottleneck? What is the flow rate?

Washing & Mixing – Flow time is 6 minutes – Flow rate is 12/6 = 2 cookies/min

Spooning the cookies – Flow time is 2 minutes – Flow rate is 12/2=6 cookies/min

Putting cookies in oven & setting Thermostat – Flow time is 1 minutes – Flow rate is 12/1= 12 cookies/min

Cooking cookies – Flow time is 9 minutes – Flow rate is 12/9= 1.333 cookies/min

Cool Down – Flow time is 5 minutes – Flow rate is 12/5= 2.4 cookies/min

Packaging them – Flow time is 2 minutes – Flow rate is 12/2= 6 cookies/min

Accepting payment – Flow time is 1 minutes – Flow rate is 12/1= 12 cookies/min

So the bottleneck is minimum of my resouces so that would be cooking cookies at 1.333 cookies/min

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