A company produces six-packs of soda cans. Each can is supposed to contain at least 12 ounces of soda.

A 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 under 72 ounces, the company is fined $100 and receives no sales revenue for the six-pack. Each six-pack sells for $3.00. It costs the company $0.02 per ounce of soda put in the cans. The company 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?

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