Bottleco 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 under 72 ounces, Bottleco is fined $100 and receives no sales revenue for the sixpack.

Each six-pack sells for $3.00. It costs Bottleco

$0.02 per ounce of soda put in the cans. Bottleco can control the mean fill rate of its soda-filling machines.

The amount put in each can by a machine is normally distributed with standard deviation 0.10 ounce.

a. Assume that the weight of each can in a six-pack has a 0.8 correlation with the weight of the other cans in the six-pack. What mean fill quantity

(within 0.05 ounce) maximizes expected profit per six-pack?

b. If the weights of the cans in the six-pack are probabilistically independent, what mean fill quantity

(within 0.05 ounce) maximizes expected profit per six-pack?

c. How can you explain the difference in the answers to parts a and b?