22. The Fizzy Company produces six-packs of soda cans.Each can is supposed to contain at least 12 ouncesof soda. If the total weight in a six-pack is less than72 ounces, Fizzy is fined $100 and receives no salesrevenue for the six-pack. Each six-pack sells for$3.00. It costs Fizzy $0.02 per ounce of soda put inthe cans. Fizzy can control the mean fill rate of itssoda-filling machines. The amount put in each canby a machine is normally distributed with standarddeviation 0.10 ounce.a. Assume that the weight of each can in a six-packhas a 0.8 correlation with the weight of the othercans in the six-pack. What mean fill quantitymaximizes expected profit per six-pack? Trymean fill rates from 12.00 to 12.35 in incrementsof 0.05.b. If the weights of the cans in the six-pack areprobabilistically independent, what mean fillquantity maximizes expected profit per six-pack?Try the same mean fill rates as in part a.c. How can you explain the difference in the answersto parts a and b?
22. The Fizzy Company produces six-packs of soda cans.
Each can is supposed to contain at least 12 ounces
of soda. If the total weight in a six-pack is less than
72 ounces, Fizzy is fined $100 and receives no sales
revenue for the six-pack. Each six-pack sells for
$3.00. It costs Fizzy $0.02 per ounce of soda put in
the cans. Fizzy can control the mean fill rate of its
soda-filling machines. The amount put in each can
by a machine is
deviation 0.10 ounce.
a. Assume that the weight of each can in a six-pack
has a 0.8
cans in the six-pack. What mean fill quantity
maximizes expected profit per six-pack? Try
mean fill rates from 12.00 to 12.35 in increments
of 0.05.
b. If the weights of the cans in the six-pack are
probabilistically independent, what mean fill
quantity maximizes expected profit per six-pack?
Try the same mean fill rates as in part a.
c. How can you explain the difference in the answers
to parts a and b?
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