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Exam 5: Extension: Decision Theory

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Question 61

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A weakness of the maximin approach is that it loses some information.

A) True
B) False

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Question 62

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The new owner of a beauty shop is trying to decide whether to hire one, two, or three beauticians. She estimates that profits next year (in thousands of dollars) will vary with demand for her services, and she has estimated demand in three categories, low, medium, and high. $\begin{array} { | l | l | l | l | } \hline { \begin{array} { l } \text { NUMBER } \\\text { OF } \\\text { BEAUTICIANS }\end{array} } & { \text { DEMAND } } \\\hline & \text { LOW } & \text { MEDIUM } & \text { HIGH } \\\hline \text { One } & 50 & 75 & 100 \\\hline \text { Two } & 0 & 100 & 100 \\\hline \text { Three } & - 100 & 70 & 300 \\\hline\end{array}$ If she feels the chances of low, medium, and high demand are 50 percent, 20 percent, and 30 percent respectively, what are the expected annual profits for the number of beauticians she will decide to hire?

A) $54,000
B) $55,000
C) $70,000
D) $80,000
E) $135,000

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

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Question 63

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Which one of these is not used in decision making under risk?

Consider the following decision scenario: $\begin{array} { c} { \text { State of Nature } } \\\begin{array} { | l | l | l | l | } \hline { } & \text { High } & \text { Med. } & \text { Low } \\\hline \text { A } & \$ 20 ^ { * } & 20 & 5 \\\hline \text { B } & 25 & 30 & 11 \\\hline \text { C } & 30 & 12 & 13 \\\hline \text { D } & 10 & 12 & 12 \\\hline \text { E } & 50 & 40 & - 28 \\\hline\end{array}\end{array}$ *PV for profits ($000) The maximax strategy would be:

The expected monetary value criterion (EMV) is the decision-making approach used with the decision environment of:

In decision theory, states of nature refer to possible future conditions.

The maximin approach involves choosing the alternative that has the "best worst" payoff.

The new owner of a beauty shop is trying to decide whether to hire one, two, or three beauticians. She estimates that profits next year (in thousands of dollars) will vary with demand for her services, and she has estimated demand in three categories, low, medium, and high. $\begin{array} { | l | l | l | l | } \hline { \begin{array} { l } \text { NUMBER } \\\text { OF } \\\text { BEAUTICIANS }\end{array} } & { \text { DEMAND } } \\\hline & \text { LOW } & \text { MEDIUM } & \text { HIGH } \\\hline \text { One } & 50 & 75 & 100 \\\hline \text { Two } & 0 & 100 & 100 \\\hline \text { Three } & - 100 & 70 & 300 \\\hline\end{array}$ If she feels the chances of low, medium, and high demand are 50 percent, 20 percent, and 30 percent respectively, what is her expected value of perfect information?

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 uses the minimax regret criterion, which size bus will he decide to purchase?

Among decision environments, risk implies that certain parameters have probabilistic outcomes.

The local operations manager for the Internal Revenue Service must decide whether to hire one, two, or three temporary tax examiners for the upcoming tax season. She estimates that net revenues (in thousands of dollars) will vary with how well taxpayers comply with the new tax code just passed by Congress, as follows: $\begin{array} { | l | l | l | l | } \hline { \begin{array} { l } \text { NUMBER } \\\text { OF } \\\text { EXAMINERS }\end{array} } & { \text { COMPLIANCE } } \\\hline & \text { LOW } & \text { NORMAL } & \text { HIGH } \\\hline \text { One } & 50 & 50 & 50 \\\hline \text { Two } & 100 & 60 & 20 \\\hline \text { Three } & 150 & 70 & - 10 \\\hline\end{array}$ If she feels the chances of low, medium, and high compliance are 20 percent, 30 percent, and 50 percent respectively, what are the expected net revenues for the number of assistants she will decide to hire?

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 would be the total payoff if script 1 were a success, but its sequel were not?

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 uses the maximin criterion, which size bus will he decide to purchase?

The Laplace criterion treats states of nature as being equally likely.

Which of the following is not an approach for decision making under uncertainty?

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 maximax criterion, which advertising strategy will she use?

Testing how a problem solution reacts to changes in one or more of the model parameters is called:

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 cancer lab?

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 feels there is a 30 percent chance that demand will be high, what are the expected monthly profits for the outlet she will decide to lease?

The new owner of a beauty shop is trying to decide whether to hire one, two, or three beauticians. She estimates that profits next year (in thousands of dollars) will vary with demand for her services, and she has estimated demand in three categories, low, medium, and high. $\begin{array} { | l | l | l | l | } \hline { \begin{array} { l } \text { NUMBER } \\\text { OF } \\\text { BEAUTICIANS }\end{array} } & { \text { DEMAND } } \\\hline & \text { LOW } & \text { MEDIUM } & \text { HIGH } \\\hline \text { One } & 50 & 75 & 100 \\\hline \text { Two } & 0 & 100 & 100 \\\hline \text { Three } & - 100 & 70 & 300 \\\hline\end{array}$ If she uses the Laplace criterion, how many beauticians will she decide to hire?