Investment advisors estimated the stock market returns for four market segments: computers, financial, manufacturing, and pharmaceuticals. Annual return projections vary depending on whether the general economic conditions are improving, stable, or declining. The anticipated annual return percentages for each market segment under each economic condition are as follows:

	Economic Condition
Market Segment	Improving	Stable	Declining
Computers	10	2	-4
Financial	8	5	-3
Manufacturing	6	4	-2
Pharmaceuticals	6	5	-1

Assume that an individual investor wants to select one market segment for a new investment. A forecast shows improving to declining economic conditions with the following probabilities: improving (0.2), stable (0.5), and declining (0.3). What is the preferred market segment for the investor, and what is the expected return percentage?

Investment advisors estimated the stock market returns for four market segments: computers, financial, manufacturing, and pharmaceuticals. Annual return projections vary depending on whether the general economic conditions are improving, stable, or declining. The anticipated annual return percentages for each market segment under each economic condition are as follows:

$$\begin{array}{lccc} & {\text { Economic Condition }} \\ \text { Market Segment } & \text { Improving } & \text { Stable } & \text { Declining } \\ \text { Computers } & 10 & 2 & -4 \\ \text { Financial } & 8 & 5 & -3 \\ \text { Manufacturing } & 6 & 4 & -2 \\ \text { Pharmaceuticals } & 6 & 5 & -1 \end{array}$$

a. Assume that an individual investor wants to select one market segment for a new investment. A forecast shows improving to declining economic conditions with the following probabilities: improving $(.2),$ stable $(.5),$ and declining $(.3).$ What is the preferred market segment for the investor, and what is the expected return percentage?
b. At a later date, a revised forecast shows a potential for an improvement in economic conditions. New probabilities are as follows: improving $(.4),$ stable $(.4),$ and declining $(.2).$ What is the preferred market segment for the investor based on these new probabilities? What is the expected return percentage?

"The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature:

$$\begin{aligned} &\text { Decision Alternative }\\ &\begin{array}{llll} d_1 & 250 & 100 & 25 \\ d_2 & 100 & 100 & 75 \end{array} \end{aligned}$$

If the decision maker knows nothing about the probabilities of the three states of nature, what is the recommended decision using the optimistic, conservative, and minimax regret approaches?"

The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature:

Construct a decision tree for this problem.

The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature:

$$\begin{aligned} &\text { Decision Alternative }\\ &\begin{array}{llll} d_1 & 250 & 100 & 25 \\ d_2 & 100 & 100 & 75 \end{array} \end{aligned}$$

Construct a decision tree for this problem.

Other members of the management team expect the Chardonnay market to become saturated at some point in the future, causing a fall in prices. Suppose that the annual profit projections fall to $\$ 50,000$ when demand for Chardonnay is strong and only Chardonnay grapes are planted. Using the original probability assessments, determine how this change would affect the optimal decision.

Seneca Hill Winery recently purchased land for the purpose of establishing a new vineyard. Management is considering two varieties of white grapes for the new vineyard: Chardonnay and Riesling. The Chardonnay grapes would be used to produce a dry Chardonnay wine, and the Riesling grapes would be used to produce a semidry Riesling wine. It takes approximately four years from the time of planting before new grapes can be harvested. This length of time creates a great deal of uncertainty concerning future demand and makes the decision about the type of grapes to plant difficult. Three possibilities are being considered: Chardonnay grapes only; Riesling grapes only; and both Chardonnay and Riesling grapes. Seneca management decided that for planning purposes it would be adequate to consider only two demand possibilities for each type of wine: strong or weak. With two possibilities for each type of wine, it was necessary to assess four probabilities. With the help of some forecasts in industry publications, management made the following probability assessments:

Revenue projections show an annual contribution to profit of $\$ 20,000$ if Seneca Hill plants only Chardonnay grapes and demand is weak for Chardonnay wine, and $\$ 70,000$ if Seneca plants only Chardonnay grapes and demand is strong for Chardonnay wine. If Seneca plants only Riesling grapes, the annual profit projection is $\$ 25,000$ if demand is weak for Riesling grapes and $\$ 45,000$ if demand is strong for Riesling grapes. If Seneca plants both types of grapes, the annual profit projections are as shown in the following table:

$$\begin{aligned} &\text { Riesling Demand }\\ &\begin{array}{lcc} \text { Chardonnay Demand } & \text { Weak } & \text { Strong } \\ \text { Weak } & \$ 22,000 & \$ 40,000 \\ \text { Strong } & \$ 26,000 & \$ 60,000 \end{array} \end{aligned}$$

What is the decision to be made, what is the chance event, and what is the consequence? Identify the alternatives for the decisions and the possible outcomes for the chance events.

"Seneca Hill Winery recently purchased land for the purpose of establishing a new vineyard. Management is considering two varieties of white grapes for the new vineyard: Chardonnay and Riesling. The Chardonnay grapes would be used to produce a dry Chardonnay wine, and the Riesling grapes would be used to produce a semidry Riesling wine. It takes approximately four years from the time of planting before new grapes can be harvested. This length of time creates a great deal of uncertainty concerning future demand and makes the decision about the type of grapes to plant difficult. Three possibilities are being considered: Chardonnay grapes only; Riesling grapes only; and both Chardonnay and Riesling grapes. Seneca management decided that for planning purposes it would be adequate to consider only two demand possibilities for each type of wine: strong or weak. With two possibilities for each type of wine, it was necessary to assess four probabilities. With the help of some forecasts in industry publications, management made the following probability assessments:

$$\begin{aligned} &\text { Riesling Demand }\\ &\begin{array}{lcc} \text { Chardonnay Demand } & \text { Weak } & \text { Strong } \\ \text { Weak } & 0.05 & 0.50 \\ \text { Strong } & 0.25 & 0.20 \end{array} \end{aligned}$$

Revenue projections show an annual contribution to profit of $20,000 if Seneca Hill plants only Chardonnay grapes and demand is weak for Chardonnay wine, and$70,000 if Seneca plants only Chardonnay grapes and demand is strong for Chardonnay wine. If Seneca plants only Riesling grapes, the annual profit projection is $25,000 if demand is weak for Riesling grapes and$45,000 if demand is strong for Riesling grapes. If Seneca plants both types of grapes, the annual profit projections are shown in the following table:

$$\begin{aligned} &\text { Riesling Demand }\\ &\begin{array}{lcc} \text { Chardonnay Demand } & \text { Weak } & \text { Strong } \\ \text { Weak } & \$ 22,000 & \$ 40,000 \\ \text { Strong } & \$ 26,000 & \$ 60,000 \end{array} \end{aligned}$$

What is the decision to be made, what is the chance event, and what is the consequence? Identify the alternatives for the decisions and the possible outcomes for the chance events"

"Seneca Hill Winery recently purchased land for the purpose of establishing a new vineyard. Management is considering two varieties of white grapes for the new vineyard: Chardonnay and Riesling. The Chardonnay grapes would be used to produce a dry Chardonnay wine, and the Riesling grapes would be used to produce a semidry Riesling wine. It takes approximately four years from the time of planting before new grapes can be harvested. This length of time creates a great deal of uncertainty concerning future demand and makes the decision about the type of grapes to plant difficult. Three possibilities are being considered: Chardonnay grapes only; Riesling grapes only; and both Chardonnay and Riesling grapes. Seneca management decided that for planning purposes it would be adequate to consider only two demand possibilities for each type of wine: strong or weak. With two possibilities for each type of wine, it was necessary to assess four probabilities. With the help of some forecasts in industry publications, management made the following probability assessments:

$$\begin{aligned} &\text { Riesling Demand }\\ &\begin{array}{lcc} \text { Chardonnay Demand } & \text { Weak } & \text { Strong } \\ \text { Weak } & 0.05 & 0.50 \\ \text { Strong } & 0.25 & 0.20 \end{array} \end{aligned}$$

Revenue projections show an annual contribution to profit of $20,000 if Seneca Hill plants only Chardonnay grapes and demand is weak for Chardonnay wine, and$70,000 if Seneca plants only Chardonnay grapes and demand is strong for Chardonnay wine. If Seneca plants only Riesling grapes, the annual profit projection is $25,000 if demand is weak for Riesling grapes and$45,000 if demand is strong for Riesling grapes. If Seneca plants both types of grapes, the annual profit projections are shown in the following table:

$$\begin{aligned} &\text { Riesling Demand }\\ &\begin{array}{lcc} \text { Chardonnay Demand } & \text { Weak } & \text { Strong } \\ \text { Weak } & \$ 22,000 & \$ 40,000 \\ \text { Strong } & \$ 26,000 & \$ 60,000 \end{array} \end{aligned}$$

Suppose management is concerned about the probability assessments when demand for Chardonnay wine is strong. Some believe it is likely for Riesling demand to also be strong in this case. Suppose the probability of strong demand for Chardonnay and weak demand for Riesling is 0.05 and that the probability of strong demand for Chardonnay and strong demand for Riesling is 0.40. How does this change the recommended decision? Assume that the probabilities when Chardonnay demand is weak are still 0.05 and 0.50."

Using the expected value approach, what is the recommended decision without perfect information? What is its expected value?

"Seneca Hill Winery recently purchased land for the purpose of establishing a new vineyard. Management is considering two varieties of white grapes for the new vineyard: Chardonnay and Riesling. The Chardonnay grapes would be used to produce a dry Chardonnay wine, and the Riesling grapes would be used to produce a semidry Riesling wine. It takes approximately four years from the time of planting before new grapes can be harvested. This length of time creates a great deal of uncertainty concerning future demand and makes the decision about the type of grapes to plant difficult. Three possibilities are being considered: Chardonnay grapes only; Riesling grapes only; and both Chardonnay and Riesling grapes. Seneca management decided that for planning purposes it would be adequate to consider only two demand possibilities for each type of wine: strong or weak. With two possibilities for each type of wine, it was necessary to assess four probabilities. With the help of some forecasts in industry publications, management made the following probability assessments:

$$\begin{aligned} &\text { Riesling Demand }\\ &\begin{array}{lcc} \text { Chardonnay Demand } & \text { Weak } & \text { Strong } \\ \text { Weak } & 0.05 & 0.50 \\ \text { Strong } & 0.25 & 0.20 \end{array} \end{aligned}$$

Revenue projections show an annual contribution to profit of $20,000 if Seneca Hill plants only Chardonnay grapes and demand is weak for Chardonnay wine, and$70,000 if Seneca plants only Chardonnay grapes and demand is strong for Chardonnay wine. If Seneca plants only Riesling grapes, the annual profit projection is $25,000 if demand is weak for Riesling grapes and$45,000 if demand is strong for Riesling grapes. If Seneca plants both types of grapes, the annual profit projections are shown in the following table:

$$\begin{aligned} &\text { Riesling Demand }\\ &\begin{array}{lcc} \text { Chardonnay Demand } & \text { Weak } & \text { Strong } \\ \text { Weak } & \$ 22,000 & \$ 40,000 \\ \text { Strong } & \$ 26,000 & \$ 60,000 \end{array} \end{aligned}$$

Develop a decision tree."

"Seneca Hill Winery recently purchased land for the purpose of establishing a new vineyard. Management is considering two varieties of white grapes for the new vineyard: Chardonnay and Riesling. The Chardonnay grapes would be used to produce a dry Chardonnay wine, and the Riesling grapes would be used to produce a semidry Riesling wine. It takes approximately four years from the time of planting before new grapes can be harvested. This length of time creates a great deal of uncertainty concerning future demand and makes the decision about the type of grapes to plant difficult. Three possibilities are being considered: Chardonnay grapes only; Riesling grapes only; and both Chardonnay and Riesling grapes. Seneca management decided that for planning purposes it would be adequate to consider only two demand possibilities for each type of wine: strong or weak. With two possibilities for each type of wine, it was necessary to assess four probabilities. With the help of some forecasts in industry publications, management made the following probability assessments:

$$\begin{aligned} &\text { Riesling Demand }\\ &\begin{array}{lcc} \text { Chardonnay Demand } & \text { Weak } & \text { Strong } \\ \text { Weak } & 0.05 & 0.50 \\ \text { Strong } & 0.25 & 0.20 \end{array} \end{aligned}$$

Revenue projections show an annual contribution to profit of $20,000 if Seneca Hill plants only Chardonnay grapes and demand is weak for Chardonnay wine, and$70,000 if Seneca plants only Chardonnay grapes and demand is strong for Chardonnay wine. If Seneca plants only Riesling grapes, the annual profit projection is $25,000 if demand is weak for Riesling grapes and$45,000 if demand is strong for Riesling grapes. If Seneca plants both types of grapes, the annual profit projections are shown in the following table:

$$\begin{aligned} &\text { Riesling Demand }\\ &\begin{array}{lcc} \text { Chardonnay Demand } & \text { Weak } & \text { Strong } \\ \text { Weak } & \$ 22,000 & \$ 40,000 \\ \text { Strong } & \$ 26,000 & \$ 60,000 \end{array} \end{aligned}$$

Use the expected value approach to recommend which alternative Seneca Hill Winery should follow in order to maximize expected annual profit."

Consider the following time series data

$$\begin{array}{l|rrrrrr} \text { Week } & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \text { Value } & 18 & 13 & 16 & 11 & 17 & 14 \end{array}$$

Use $\alpha=0.2$ to compute the exponential smoothing values for the time series. Compute MSE and a forecast for week 7.

Consider the following time series:

$$\begin{array}{l|rrrrr} \text{t} & 1 & 2 & 3 & 4 & 5 \\ \hline \text{y}_{\text{t}} & 6 & 11 & 9 & 14 & 15 \end{array}$$

Construct a time series plot. What type of pattern exists in the data?