Question 1

A plant manager wants to know how much he should be willing to pay for perfect market research. Currently there are two states of nature facing his decision to expand or do nothing. Under favorable market conditions the manager would make $100,000 for the large plant and $5,000 for the small plant. Under unfavorable market conditions the large plant would lose $50,000 and the small plant would make $0. If the two states of nature are equally likely, how much should he pay for perfect information?

Accepted Answer

The expected value of the decision without perfect information is:
E(DO NOTHING) = (0.5)($0) + (0.5)($5,000) = $2,500
E(EXPAND) = (0.5)($100,000) + (0.5)(-$50,000) = $25,000

The expected value of the decision with perfect information is:
If the manager finds out that the market will be favorable, he will choose to expand the large plant and make $100,000. If the market will be unfavorable, he will choose to do nothing and only make $5,000. Therefore, the manager would be willing to pay up to the difference between the expected value with perfect information and the expected value without perfect information:
E(PERFECT INFO) = (0.5)($100,000) + (0.5)($5,000) = $52,500
Max amount to pay for perfect info = E(PERFECT INFO) - E(DO NOTHING) = $52,500 - $2,500 = $25,000. 
Therefore, the manager should be willing to pay up to $25,000 for perfect information.

Question 2

Doing nothing would yield how much profit if favorable market conditions prevail according to the following decision table $$\begin{array} { | l | l | l | } 
\hline \text { Alternative } & \text { Favorable market } & \text { Unfavorable Market } \
\hline \text { Do Nothing } & \$ 20,000 & - \$ 10,000 \
\hline
\end{array}$$

Accepted Answer

If favorable market conditions prevail, doing nothing would yield a profit of $20,000 according to the decision table.

Question 3

A tabular presentation that shows the outcome for each decision alternative under the various possible states of nature is called a(n)

Accepted Answer

The payoff table is the appropriate tool for comparing the outcome of each decision alternative under the different possible states of nature. It allows for a clear analysis of the best option based on the potential outcomes and probabilities associated with each state of nature.

Question 4

A decision-maker using the maximin criterion on the problem below would choose Alternative ________ because the maximum of the row minimums is ________. States of Nature
$$\begin{array} { | c | c | c | c | } 
\hline & 1 & 2 & 3 \
\hline \text { Alternative A } & 50 & 55 & 60 \
\hline \text { Alternative B } & 30 & 50 & 80 \
\hline \text { Alternative C } & 70 & 80 & 70 \
\hline \text { Alternative D } & - 100 & - 10 & 140 \
\hline
\end{array}$$

Accepted Answer

The answer of A decision-maker using the maximin criterion on...

Question 5

The expected value of perfect information (EVPI) is the

Accepted Answer

The expected value of perfect information (EVPI) is the difference between the payoff under perfect information and the payoff under risk, and represents the maximum amount a decision maker should be willing to pay to obtain perfect information. Option A is incorrect because payoff for a decision made under perfect information is called the expected value with perfect information (EVwPI). Option B and E are incorrect because they relate to decision-making under minimum and maximum risk, respectively, which are not the same as the EVPI. Option C is incorrect because it refers to the average expected payoff, which is not the same as the EVPI.

Question 6

When solving decision trees, what phrase represents the act of dropping an alternative from consideration because it is less favorable than another available option?

Accepted Answer

"Prune the branch" is a commonly used phrase in decision tree analysis to represent dropping an alternative from consideration because it is less favorable than another available option.

Question 7

The difference between the expected payoff under perfect information and the maximum expected payoff under risk is

Accepted Answer

The difference between the expected payoff under perfect information and the maximum expected payoff under risk is known as the expected value of perfect information (EVPI). It measures the value of additional information when making a decision.

Question 8

The following decision tree has how many state of nature nodes?

Accepted Answer

The answer of The following decision tree has how many...

Question 9

What is the EMV for Option 1 in the following decision table? States of Nature
$$\begin{array} { | c | c | c | } 
\hline \text { Alternatives } & \mathrm { S } _ { 1 } & \mathrm {~S} _ { 2 } \
\hline \mathrm { p } & .3 & .7 \
\hline \text { Option } 1 & 15,000 & 20,000 \
\hline \text { Option } 2 & 10,000 & 30,000 \
\hline
\end{array}$$

Accepted Answer

The answer of What is the EMV for Option 1...

Question 10

In terms of decision theory, an occurrence or situation over which the decision maker has no control is called a(n)

Accepted Answer

A state of nature is an occurrence or situation over which the decision maker has no control. A decision under uncertainty refers to a situation where the decision maker is unsure about the likelihood of different outcomes. A decision tree is a graphical representation of the possible outcomes of a decision. An alternative is a possible option or course of action. A probable state is not a recognized term in decision theory.

Question 11

The expected value with perfect information

Accepted Answer

The expected value with perfect information (EVwPI) is the expected value that would result if the decision maker had perfect information about the uncertain event. This means that the probability and outcome of each possible scenario are known with certainty. EVwPI is an input into the calculation of the expected value of perfect information (EVPI), which is the maximum amount a decision maker should be willing to pay for perfect information. EVPI equals the EVwPI minus the expected monetary value (EMV) of the decision without perfect information. Choice A is incorrect because EVPI is not equal to EVwPI minus EMV, but rather EVPI equals EVwPI minus EMV. Choice B is incorrect because it is possible to calculate EVwPI even if each decision alternative does not have a known probability of occurrence. Choice D is incorrect because the expected value with perfect information is not the average of the maximax and the maximin. Choice E is incorrect because answer C is correct.

Question 12

A decision-maker using the maximax criterion on the problem below would choose Alternative ________ because the maximum of the row maximums is ________. States of Nature
$$\begin{array} { | c | c | c | c | } 
\hline & 1 & 2 & 3 \
\hline \text { Alternative A } & 50 & 55 & 60 \
\hline \text { Alternative B } & 30 & 50 & 80 \
\hline \text { Alternative C } & 70 & 80 & 70 \
\hline \text { Alternative D } & - 100 & - 10 & 140 \
\hline
\end{array}$$

Accepted Answer

The maximax criterion involves selecting the alternative with the highest possible payoff. For Alternative D, the maximum payoff is 140, which is the highest among all alternatives.

Question 13

The highest value for the equally likely criterion is ________; this occurs with alternative ________. States of Nature
$$\begin{array} { | c | c | c | } 
\hline \text { Alternatives } & \mathrm { S } _ { 1 } & \mathrm {~S} _ { 2 } \
\hline \text { Option } 1 & \$ 10,000 & \$ 30,000 \
\hline \text { Option } 2 & \$ 5,000 & \$ 45,000 \
\hline \text { Option } 3 & - \$ 4,000 & \$ 60,000 \
\hline
\end{array}$$

Accepted Answer

The answer of The highest value for the equally likely...

Question 14

The expected value with perfect information is

Accepted Answer

The expected value with perfect information is the average return obtained when the decision maker knows which state of nature is going to occur before the decision is made. It assumes the decision maker has perfect information about the future outcomes, allowing them to choose the option with the highest expected value.

Question 15

The decision criterion that would be used by an optimistic decision maker solving a problem under conditions of uncertainty would be the

Accepted Answer

An optimistic decision maker would choose the maximax criterion, which maximizes the potential maximum outcome. This decision maker is willing to take risks and ignore potential losses, and therefore, aims to achieve the highest possible gain rather than considering the probability of different outcomes.

Question 16

The outcome of an alternative/state of nature combination is a(n)

Accepted Answer

The outcome of an alternative/state of nature combination is referred to as a conditional value, which is the result or payoff associated with a specific decision under a particular state of nature.

Question 17

Expected monetary value is most appropriate for problem solving that takes place

Accepted Answer

The answer of Expected monetary value is most appropriate for...

Question 18

The likelihood that a decision maker will ever receive a payoff precisely equal to the EMV when making any one decision is

Accepted Answer

The EMV is an expected value based on probabilities of different outcomes, and it is rare for the actual outcome to match the expected value precisely. Therefore, the likelihood of receiving a payoff precisely equal to the EMV is low.

Question 19

There are three equally likely states of nature (High, Medium, and Low demand). If the large factory will post profits of $50,000, $25,000, and - $10,000 under these states of nature, respectively, what is the EMV of the factory?

Accepted Answer

The EMV (Expected Monetary Value) is calculated by multiplying each outcome by its probability and summing the results: (1/3 * $50,000) + (1/3 * $25,000) + (1/3 * -$10,000) = $21,666.67.

Question 20

A decision maker who uses the maximin criterion when solving a problem under conditions of uncertainty is

Accepted Answer

A decision maker who uses the maximin criterion when solving a problem under conditions of uncertainty is a pessimist. Maximin assumes that the worst possible outcome will occur and the decision maker should choose the alternative that maximizes the minimum payoff. This criterion is appropriate for a risk-averse decision maker who is more concerned about avoiding the worst outcome than achieving the best possible outcome.

Quiz 18: Decision-Making Tools