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arock1 arock1
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5 years ago
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?
 
  (B) If the weights of the cans in the six-pack are probabilistically independent, what mean fill quantity (within 0.05 ounce) will maximize expected profit per six-pack?
 
  (C) How can you explain the difference in the answers for (A) and (B)?
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shahanasshahanas
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5 years ago Edited: 4 years ago, bio_man
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(A) With correlated values, the mean profit is maximized somewhere around a 12.26 mean fill rate.

(B) With independent values, the mean profit is maximized somewhere around a 12.14 mean fill rate.

(C) With uncorrelated values, the mean profit is maximized at a much mean lower fill rate of around 12.14. The reason is that we're trying to avoid the penalty cost. With correlated values, if one can be low, the others tend to be low, which increases the chances of the penalty. To compensate for this, we need to make the mean fill rate larger.
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arock1 Author
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#2
5 years ago
You are always so helpful
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