Question 1

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

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

Question 2

The expected value with perfect information

Accepted Answer

The expected value with perfect information (EVwPI) is the maximum expected value that can be obtained when full information is available. It is an input into the calculation of the expected value of perfect information (EVPI). EVwPI assumes that each decision alternative has a known probability of occurrence. Therefore, choice B is incorrect. The formula for EVwPI is EVwPI = EMV with perfect information - EMV. Therefore, choice A is incorrect. The average of the maximax and the maximin is known as the Hurwicz criterion, not the EVwPI. Therefore, choice D is incorrect.

Question 3

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

Accepted Answer

The maximin criterion is used by decision makers who adopt a pessimistic outlook and focus on the worst-case scenario. They assume that the worst possibility will happen and make decisions based on minimizing the maximum possible loss.

Question 4

The following decision tree has how many state of nature nodes

Accepted Answer

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

Question 5

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 represents the maximum amount a decision-maker would be willing to pay to acquire additional information that would eliminate all uncertainty. Therefore, option C, expected value of perfect information, is the best choice. The other options are not related to the concept of EVPI.

Question 6

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.

Question 7

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 8

The expected value of perfect information (EVPI) is the

Accepted Answer

EVPI is the difference between the payoff under perfect information and the payoff under risk. It represents the maximum amount an individual should be willing to pay for additional information to make a better decision.

Question 9

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 10

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

Accepted Answer

A payoff table shows the potential outcomes of each decision alternative under different states of nature, making it easier to compare the options and make a decision. Therefore, it is the best choice for this situation. The other options listed are not relevant to this scenario.

Question 11

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

Accepted Answer

The maximax criterion involves choosing the alternative with the highest possible payoff. For each alternative, the maximum payoff is: A: 60, B: 80, C: 80, D: 140. Alternative D has the highest maximum payoff of 140.

Question 12

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

Accepted Answer

The maximax criterion is used by an optimistic decision maker as it selects the decision alternative that results in the maximum possible payoff. This criterion assumes that the best possible outcome will occur and ignores the probabilities of the various outcomes, which aligns with an optimistic decision maker's approach.

Question 13

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

Accepted Answer

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

Question 14

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 a theoretical value based on probabilities and payoffs, and it is unlikely that any decision maker will receive a payoff that is exactly equal to this value. Real-world outcomes are subject to various uncertainties and unforeseen events. Therefore, the likelihood that a decision maker will receive a payoff precisely equal to the EMV is low, near 0%.

Question 15

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

Accepted Answer

The maximin criterion involves choosing the alternative with the highest minimum payoff. In this problem, the minimum payoffs for each alternative are:

A: 10
B: 20
C: 40
D: 5

The maximum of these minimums is 40, which is achieved by Alternative C. Therefore, the decision-maker would choose Alternative C using the maximin criterion.

Question 16

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 common phrase used in decision trees to represent the act of dropping an alternative. It fits well with the metaphor of a tree, where branches represent different options and decisions.

Question 17

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 in the context of a particular state of nature.

Question 18

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 refers to a situation or event that is beyond the control of the decision maker, and decision makers can only assign probabilities to different states of nature. The other options, decision under uncertainty, decision tree, and alternative, do not specifically refer to situations outside the control of the decision maker.

Question 19

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:

Expected value of expanding = (0.5 x $100,000) + (0.5 x -$50,000) = $25,000
Expected value of doing nothing = (0.5 x $5,000) + (0.5 x $0) = $2,500

If the plant manager has perfect information about the market conditions, he can make the decision with certainty and avoid the possibility of a loss. Therefore, he should be willing to pay up to the amount of the difference between the expected values, which is:

$25,000 - $2,500 = $22,500

Therefore, the plant manager should be willing to pay up to $22,500 for perfect information. Since this value is closest to option B, that is the correct answer.

Question 20

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

Accepted Answer

The equally likely criterion implies that each option is equally likely to be chosen. Therefore, we need to calculate the expected payoffs of each option and choose the maximum payoff.

Option 1: (0.2)(10,000) + (0.8)(5,000) = 6,000
Option 2: (0.5)(25,000) + (0.5)(15,000) = 20,000
Option 3: (0.3)(28,000) + (0.7)(10,000) = 13,600

Therefore, the highest value for the equally likely criterion is $20,000 and it occurs with alternative Option 2.

Quiz 21: Decision-Making Tools