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Exam 5: Extension: Decision Theory

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Question 41

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Two professors at a nearby university want to coauthor a new textbook in either economics or statistics. They feel that if they write an economics book, they have a 50 percent chance of placing it with a major publisher, and it should ultimately sell about 40,000 copies. If they cannot get a major publisher to take it, then they feel they have an 80 percent chance of placing it with a smaller publisher, with ultimate sales of 30,000 copies. On the other hand, if they write a statistics book, they feel they have a 40 percent chance of placing it with a major publisher, and it should result in ultimate sales of about 50,000 copies. If they cannot get a major publisher to take it, they feel they have a 50 percent chance of placing it with a smaller publisher, with ultimate sales of 35,000 copies. What is the probability that the economics book would wind up being placed with a smaller publisher?

A) .8
B) .5
C) .4
D) .2
E) .1

F) A) and B)
G) D) and E)

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Question 42

Multiple Choice

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The owner of Tastee Cookies needs to decide whether to lease a small, medium, or large new retail outlet. She estimates that monthly profits will vary with demand for her cookies as follows: $\begin{array}{|l|l|l|l|}\hline\text {SIZE}\\\text {OF}&\text {DEMAND}\\\hline \text { OUTLET } & \text { LOW } && \text { HIGH } \\\hline \text { Small } & \$ 1,000 && 1,000 \\\hline \text { Medium } & 500 && 2,500 \\\hline \text { Large } & 0 && 3,000 \\\hline\end{array}$ If she uses the maximax criterion, what size outlet will she decide to lease?

A) small
B) medium
C) large
D) either small or medium
E) either medium or large

F) A) and C)
G) None of the above

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Question 43

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The maximin approach to decision making refers to:

The expected monetary value approach is most appropriate when the decision maker is risk neutral.

The operations manager for a well-drilling company must recommend whether to build a new facility, expand his existing one, or do nothing. He estimates that long-run profits (in $000) will vary with the amount of precipitation (rainfall) as follows: $\begin{array} { | l | l | l | l | } \hline { \text { ALTERNATIVE } } & { \text { PRECIPITATION } } \\\hline& \text { LOW } & \text { NORMAL } & \text { HIGH } \\\hline \text { Do Nothing } & - 100 & 100 & 300 \\\hline \text { Expand } & 350 & 500 & 200 \\\hline \text { Build New } & 750 & 300 & 0 \\\hline\end{array}$ If he uses the Laplace criterion, which alternative will he decide to select?

The owner of Tastee Cookies needs to decide whether to lease a small, medium, or large new retail outlet. She estimates that monthly profits will vary with demand for her cookies as follows: $\begin{array}{|l|l|l|l|}\hline\text {SIZE}\\\text {OF}&\text {DEMAND}\\\hline \text { OUTLET } & \text { LOW } && \text { HIGH } \\\hline \text { Small } & \$ 1,000 && 1,000 \\\hline \text { Medium } & 500 && 2,500 \\\hline \text { Large } & 0 && 3,000 \\\hline\end{array}$ If she uses the minimax regret criterion, what size outlet will she decide to lease?

A decision maker's worst option has an expected value of $1,000, and her best option has an expected value of $3,000. With perfect information, the expected value would be $5,000. What is the expected value of perfect information?

The head of operations for a movie studio wants to determine which of two new scripts they should select for their next major production. (Due to budgeting constraints, only one new picture can be undertaken at this time.) She feels that script 1 has a 70 percent chance of earning about $10,000,000 over the long run, but a 30 percent chance of losing $2,000,000. If this movie is successful, then a sequel could also be produced, with an 80 percent chance of earning $5,000,000, but a 20 percent chance of losing $1,000,000. On the other hand, she feels that script 2 has a 60 percent chance of earning $12,000,000, but a 40 percent chance of losing $3,000,000. If successful, its sequel would have a 50 percent chance of earning $8,000,000, but a 50 percent chance of losing $4,000,000. Of course, in either case, if the original movie were a flop, then no sequel would be produced. What is the expected value for the optimum decision alternative?

Two professors at a nearby university want to coauthor a new textbook in either economics or statistics. They feel that if they write an economics book, they have a 50 percent chance of placing it with a major publisher, and it should ultimately sell about 40,000 copies. If they cannot get a major publisher to take it, then they feel they have an 80 percent chance of placing it with a smaller publisher, with ultimate sales of 30,000 copies. On the other hand, if they write a statistics book, they feel they have a 40 percent chance of placing it with a major publisher, and it should result in ultimate sales of about 50,000 copies. If they cannot get a major publisher to take it, they feel they have a 50 percent chance of placing it with a smaller publisher, with ultimate sales of 35,000 copies. What is the expected value for the decision alternative to write the statistics book?

The advertising manager for Roadside Restaurants, Inc., needs to decide whether to spend this month's budget for advertising on print media, television, or a mixture of the two. She estimates that the cost per thousand "hits" (readers or viewers) will vary depending upon the success of the new cable television network she plans to use, as follows: $\begin{array} { | l | l | l | l|} \hline { \text { Strategy } } & { \text { Cable Network } } \\\hline & \text { Successful } & &\text { Failure } \\ \hline \text { Print } & \$ 10 && 10 \\\hline \text { Mixed } & 4 & &14 \\\hline \text { Television } & 1 && 21 \\\hline\end{array}$ If she uses the minimax regret criterion, which advertising strategy will she use?

One local hospital has just enough space and funds currently available to start either a cancer or heart research lab. If administration decides on the cancer lab, there is a 20 percent chance of getting $100,000 in outside funding from the American Cancer Society next year, and an 80 percent chance of getting nothing. If the cancer research lab is funded the first year, no additional outside funding will be available the second year. However, if it is not funded the first year, then management estimates the chances are 50 percent it will get $100,000 the following year, and 50 percent that it will get nothing again. If, however, the hospital's management decides to go with the heart lab, then there is a 50 percent chance of getting $50,000 in outside funding from the American Heart Association the first year and a 50 percent change of getting nothing. If the heart lab is funded the first year, management estimates a 40 percent chance of getting another $50,000 and a 60 percent chance of getting nothing additional the second year. If it is not funded the first year, then management estimates a 60 percent chance for getting $50,000 and a 40 percent chance for getting nothing in the following year. For both the cancer and heart research labs, no further possible funding is anticipated beyond the first two years. What is the expected value for the decision alternative to select the heart lab?

Consider the following decision scenario: $\begin{array} { | l | l | l | l | l | } \hline { \text { Alternative } } & { \text { State of Nature } } & & \\\hline & \# 1 & \# 2 & \# 3 & \# 4 \\ \hline \text { A } & 1 & 0 & 1 & 6 \\\hline \text { B } & 1 & 5 & 4 & 2 \\\hline \text { C } & 3 & 2 & 2 & 3 \\\hline\end{array}$ If you are uncertain which state of nature will occur, and use the maximin criterion, which alternative will you select?

The construction manager for Acme Construction, Inc., must decide whether to build single-family homes, apartments, or condominiums. He estimates annual profits (in $000) will vary with the population trend as follows: $\begin{array} { | l | l | l | l | } \hline { \text { Type } } & { \text { POPULATION TREND } } \\\hline & \text { Declining } & \text { Stable } & \text { Growing } \\ \hline \text { Single Family } & 200 & 90 & 70 \\\hline \text { Apartments } & 70 & 170 & 90 \\\hline \text { Condos } & - 20 & 100 & 220 \\\hline\end{array}$ If he uses the Laplace criterion, which kind of dwellings will he decide to build?

The construction manager for Acme Construction, Inc., must decide whether to build single-family homes, apartments, or condominiums. He estimates annual profits (in $000) will vary with the population trend as follows: $\begin{array} { | l | l | l | l | } \hline { \text { Type } } & { \text { POPULATION TREND } } \\\hline & \text { Declining } & \text { Stable } & \text { Growing } \\ \hline \text { Single Family } & 200 & 90 & 70 \\\hline \text { Apartments } & 70 & 170 & 90 \\\hline \text { Condos } & - 20 & 100 & 220 \\\hline\end{array}$ If he uses the maximin criterion, which kind of dwellings will he decide to build?

The term "opportunity loss or regret" is most closely associated with:

The operations manager for a local bus company wants to decide whether he should purchase a small, medium, or large new bus for his company. He estimates that the annual profits (in $000) will vary depending upon whether passenger demand is low, medium, or high, as follows: $\begin{array} { | l | l | l | l | } \hline \text { Bus } & { \text { DEMAND } } \\\hline & \text { LOW } & \text { MEDIUM } & \text { HIGH } \\ \hline \text { Small } & 50 & 60 & 70 \\\hline \text { Medium } & 40 & 80 & 90 \\\hline \text { Large } & 20 & 50 & 120 \\\hline\end{array}$ If he feels the chances of low, medium, and high demand are 30 percent, 30 percent, and 40 percent respectively, what is his expected value of perfect information?

Two professors at a nearby university want to coauthor a new textbook in either economics or statistics. They feel that if they write an economics book, they have a 50 percent chance of placing it with a major publisher, and it should ultimately sell about 40,000 copies. If they cannot get a major publisher to take it, then they feel they have an 80 percent chance of placing it with a smaller publisher, with ultimate sales of 30,000 copies. On the other hand, if they write a statistics book, they feel they have a 40 percent chance of placing it with a major publisher, and it should result in ultimate sales of about 50,000 copies. If they cannot get a major publisher to take it, they feel they have a 50 percent chance of placing it with a smaller publisher, with ultimate sales of 35,000 copies. What is the expected value for the optimum decision alternative?

The advertising manager for Roadside Restaurants, Inc., needs to decide whether to spend this month's budget for advertising on print media, television, or a mixture of the two. She estimates that the cost per thousand "hits" (readers or viewers) will vary depending upon the success of the new cable television network she plans to use, as follows: $\begin{array} { | l | l | l | l|} \hline { \text { Strategy } } & { \text { Cable Network } } \\\hline & \text { Successful } & &\text { Failure } \\ \hline \text { Print } & \$ 10 && 10 \\\hline \text { Mixed } & 4 & &14 \\\hline \text { Television } & 1 && 21 \\\hline\end{array}$ For what range of probability that the new cable network will be successful will she select the mixed media strategy?

When a decision-making scenario involves two or more departments, if the individual departments pursue what is optimal for them, sometimes the overall organization suffers. This is an example of:

Determining the average payoff for each alternative and choosing the alternative with the highest average is the approach called: