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Homework answers / question archive / A fish market sells fresh fish and seafood
A fish market sells fresh fish and seafood. The market receives daily shipments of farm-raised trout from a nearby supplier. Each trout costs $2.25 and is sold for $4.05. To maintain its reputation for freshness, at the end of the day the market sells any leftover trout to a local pet food manufacturer for $1.35 each. The owner of the market wants to determine how many trout to order each day. Historically, the daily demand for trout is:
Demand 10 11 12 13 14 15 16 17 18 19 20
Probability 0.02 0.06 0.09 0.11 0.13 0.15 0.18 0.11 0.07 0.05 0.03
Construct a payoff matrix for this problem.
(a)
What decision should be made according to the maximax decision rule? That is, how many trout should be ordered?
(b)
What decision should be made according to the maximin decision rule? That is, how many trout should be ordered?
(c)
What decision should be made according to the minimax regret decision rule? That is, how many trout should be ordered?
(d)
What decision should be made according to the EMV decision rule? That is, how many trout should be ordered?
(e)
What decision should be made according to the EOL decision rule? That is, how many trout should be ordered?
(f)
At most, how much should the owner of the market be willing to pay (in dollars) to obtain a demand forecast that is 100% accurate? (Round your answer to the nearest cent.)
$
(g)
Which decision rule would you recommend the market use in this case? Why?
This answer has not been graded yet.
(h)
Suppose that the market receives a quantity discount that reduces the price to $2.05 per trout if it purchases 15 or more. Using the EMV decision rule, how many trout would you recommend the owner of the fish house order each day in this case?
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2.
[–/6 Points]
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RAGSMDA9 14.E.013.
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The Tall Oaks Wood Products Company is considering purchasing timberland for $5 million that would provide a future source of timber supply for the company's operations over the next 10 years. Alternatively, for $5 million, the company could also buy timber as needed on the open market. The future cash flows from using the timber are estimated to have a present value of $6 million regardless of whether the company buys the timberland today or waits to purchase its timber as needed over the next 10 years. This means there is a $1 million net present value (NPV) of either buying the timberland now or buying the timber as needed. In other words, from a financial standpoint, the two alternative timber acquisition strategies would be equal. Now suppose that the company believes there is only a 60% chance that the environmental regulations affecting timber supply will remain unchanged. Furthermore, the company believes that there is a 35% chance these regulations will become stricter during the next 10 years and only a 5% chance that these regulations will be relaxed. A reduction in timber supply should cause an increase in both the present value of future cash flows from using the timber due to higher sales prices and an increase in the present value of the cost of purchasing the timber as needed. (Of course, the change in selling price and buying cost may not be equal.) Should regulations become stricter, the company believes the NPV from buying the timberland now would increase to $1.8 million while an NPV of buying the timber as needed would decrease to −$0.6 million. Increases in the timber supply should have effects in the opposite direction. Thus, should regulations become less strict, the company believes the NPV from buying the timberland now would decrease to −$0.3 million while an NPV of buying the timber as needed would increase to $1.4 million.
(a)
Construct a payoff matrix for this problem.
Environmental Regulations
Alternatives: No Change Tightened Relaxed
Buy Now
Buy As Needed
(b)
What decision should be made according to the maximax decision rule?
The company should buy as needed.
The company should buy now.
The decision rule results in a tie.
(c)
What decision should be made according to the maximin decision rule?
The company should buy as needed.
The company should buy now.
The decision rule results in a tie.
(d)
What decision should be made according to the minimax regret decision rule?
The company should buy as needed.
The company should buy now.
The decision rule results in a tie.
(e)
What decision should be made according to the EMV decision rule?
The company should buy as needed.
The company should buy now.
The decision rule results in a tie.
(f)
What decision should be made according to the EOL decision rule?
The company should buy as needed.
The company should buy now.
The decision rule results in a tie.
(g)
Construct a decision tree for this problem.
Decision Tree
buy timberland nowbuy timber as neededno regulatory changeprobability =
NPV =
tightened regulationsprobability =
NPV =
relaxed regulationsprobability =
NPV =
no regulatory changeprobability =
NPV =
tightened regulationsprobability =
NPV =
relaxed regulationsprobability =
NPV =
A decision tree has 12 answer blanks. Refer to the adjacent list for more details.
Description
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3.
[–/4 Points]
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RAGSMDA9 14.E.015.
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A manufacturer has two machines that make the same parts for diesel truck engines. One machine is 5 years older than the other one. The older machine runs slower and makes 37% of the parts, of which 86% are of acceptable quality and don't require rework. Only 7% of the parts made by the newer machine require rework.
If a part is found to be out of specification and in need of rework, what is the probability that it was made by the older machine? (Round your answer to four decimal places.)
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4.
[–/4 Points]
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RAGSMDA9 14.E.023.
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From industry statistics, a credit card company knows that 80% of its potential card holders are good credit risks and 20% are bad credit risks. The company uses discriminant analysis to screen credit card applicants and determine which ones should receive credit cards. The company awards credit cards to 70% of those who apply. The company has found that of those awarded credit cards, 88.8% turn out to be good credit risks. What is the probability that an applicant who is a bad credit risk will be denied a credit card?
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[–/4 Points]
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RAGSMDA9 14.E.025.
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A company has developed a new type of hand lotion with a distinctive fragrance. Before distributing it nationally, the company will test market the new product. The joint probability of a successful test market and high sales upon national distribution is 0.5. The joint probability of a successful test market and low sales nationally is 0.08. The joint probabilities of an unsuccessful test market and either high or low sales are both 0.21.
(a)
Use this data to construct a joint probability table.
Joint Probabilities
High Sales Low Sales Total
Successful Response
Unsuccessful Response
Total
(b)
What is the marginal probability of a successful test market?
(c)
What is the conditional probability of high sales given a successful test market? (Round your answer to four decimal places.)
(d)
What is the conditional probability of a successful test market given that the product is destined for high sales nationally? (Round your answer to four decimal places.)
