Calculus Student
Franklin & Marshall College
Lancaster, PA 17604
Dear Calculus Student:
I have a difficult problem for which no one in my factory can find a solution,
and I hope that you can help me. Your intrepid and enterprising professor, Dr.
Crannell, referred me to you.
At the Jumping Gelatin Factory, we make 42 different flavors of gelatin and
provide all the gelatin for all the local day-care centers and nursing homes,
as well as for numerous fraternity and sorority parties. Because of this,
turnaround time is extremely important to us, and lately we have become
increasingly worried about the amount of time it takes to mix and cool our food
product.
As you may know from making gelatin at home, the preparation process
is this: The gelatin powder is added to a quantity of boiling water and stirred
at the same temperature until it dissolves. We have experimented with the time
needed at this stage and have discovered that 2 minutes is the shortest amount
of time we can take and still maintain the high quality of our dessert.
The next stage is to remove the gelatin from the burner. At this point we add
ice water (the same amount as the boiling water) and wait for the dessert to
gel. It is at this stage that we are hoping to improve our efficiency. There
are some people here who believe that the ice water should be added immediately;
others believe that it should be added bit-by-bit; and still others believe we
should wait an hour and then add the ice water.
No matter which of these procedures we use, national gelatin guidelines
proscribe that one hour after the gelatin is dissolved, we must place the entire
mixture into a refrigerator and remove it only again when gelled. Of course,
the cooler it is by this point, the faster it gels. The refrigeration
temperature is also mandated, and so that can not be changed.
The question I have for you is: Given the procedure described above, in what
manner should we add the cold water to cool the mixture the fastest? I would
appreciate an answer as soon as possible, but hopefully no later than September
30, (our budget is due the day after).
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