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 semi-dry 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 concerning 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.

$$\begin{matrix} \text{ } & \text{Riesling} & \text{Demand}\\ \text{Chardonnay Demand} & \text{Weak} & \text{Strong}\\ \text{Weak} & \text{.05} & \text{.50}\\ \text{Strong} & \text{.25} & \text{.20}\\ \end{matrix}$$

Revenue projections show an annual contribution to profit of $20,000 if Seneca Hill only plants Chardonnay grapes and demand is weak for Chardonnay wine, and$70,000 if they only plant Chardonnay grapes and demand is strong for Chardonnay wine. If they only plant 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.

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

a. 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. b. Develop a decision tree. c. Use the expected value approach to recommend which alternative Seneca Hill Winery should follow in order to maximize expected annual profit. d. 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 .05 and that the probability of strong demand for Chardonnay and strong demand for Riesling is .40. How does this change the recommended decision? Assume that the probabilities when Chardonnay demand is weak are still .05 and .50. e. 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 Chardonnay grapes only are planted. Using the original probability assessments, determine how this change would affect the optimal decision.

The Gorman Manufacturing Company must decide whether to manufacture a component part at its Milan, Michigan, plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit (in thousands of dollars).

$$\begin{matrix} \text{ } & \text{ } & \text{State of Nature}\\ \text{ } & \text{Low Demand} & \text{Medium Demand} & \text{High Demand}\\ \hline \text{Decision Alternative} & \text{s1} & \text{s2} & \text{s3}\\ \text{Manufacture, d1} & \text{-20} & \text{40} & \text{100}\\ \text{Purchase, d2} & \text{10} & \text{45} & \text{70}\\ \end{matrix}$$

The state-of-nature probabilities are $P \left( s _ { 1 } \right) = .35 , P \left( s _ { 2 } \right) = .35 ,$ and $P \left( s _ { 3 } \right) = .30$. a. Use a decision tree to recommend a decision. b. Use EVPI to determine whether Gorman should attempt to obtain a better estimate of demand. c. A test market study of the potential demand for the product is expected to report either a favorable (F) or unfavorable (U) condition. The relevant conditional probabilities are as follows:

$$\begin{array} { l l } { P ( F | s _ { 1 } ) = .10 } & { P ( U | s _ { 1 } ) = .90 } \\ { P ( F | s _ { 2 } ) = .40 } & { P ( U | s _ { 2 } ) = .60 } \\ { P ( F | s _ { 3 } ) = .60 } & { P ( U | s _ { 3 } ) = .40 } \end{array}$$

What is the probability that the market research report will be favorable? d. What is Gorman’s optimal decision strategy? e. What is the expected value of the market research information?

"Amy Lloyd is interested in leasing a new Honda and has contacted three automobile dealers for pricing information. Each dealer offered Amy a closed-end 36-month lease with no down payment due at the time of signing. Each lease includes a monthly charge and a mileage allowance. Additional miles receive a surcharge on a per-mile basis. The monthly lease cost, the mileage allowance, and the cost for additional miles follow:

$$\begin{aligned} &\text { Cost per }\\ &\begin{array}{lccc} {\text { Dealer }} & \text { Monthly Cost } & \text { Mileage Allowance } & \text { Additional Mile } \\ \text { Hepburn Honda } & \$ 299 & 36,000 & \$ 0.15 \\ \text { Midtown Motors } & \$ 310 & 45,000 & \$ 0.20 \\ \text { Hopkins Automotive } & \$ 325 & 54,000 & \$ 0.15 \end{array} \end{aligned}$$

Amy decided to choose the lease option that will minimize her total 36 -month cost. The difficulty is that Amy is not sure how many miles she will drive over the next three years. For purposes of this decision, she believes it is reasonable to assume that she will drive 12,000 miles per year, 15,000 miles per year, or 18,000 miles per year. With this assumption Amy estimated her total costs for the three lease options. For example, she figures that the Hepburn Honda lease will cost her $36(\$ 299)+\$ 0.15(36,000-36,000)=\$ 10,764$ if she drives 12,000 miles per year, 36( $\$ 299)+\$ 0.15(45,000-36,000)=\$ 12,114$ if she drives 15,000 miles per year, or $36(\$ 299)+\$ 0.15(54,000-36,000)=\$ 13,464$ if she drives 18,000 miles per year.

If Amy has no idea which of the three mileage assumptions is most appropriate, what is the recommended decision (leasing option) using the optimistic, conservative, and minimax regret approaches?"

Myrtle Air Express decided to offer direct service from Cleveland to Myrtle Beach. Management must decide between a full price service using the company’s new fleet of jet aircraft and a discount service using smaller capacity commuter planes. It is clear that the best choice depends on the market reaction to the service Myrtle Air offers. Management developed estimates of the contribution to profit for each type of service based upon two possible levels of demand for service to Myrtle Beach: strong and weak. The following table shows the estimated quarterly profits (in thousands of dollars).

$$\begin{matrix} \text{ } & \text{Demand} & \text{for Service}\\ \hline \text{Service} & \text{Strong} & \text{Weak}\\ \text{Full price} & \text{\$960} & \text{-\$490}\\ \text{Discount} & \text{\$670} & \text{\$320}\\ \end{matrix}$$

a. What is the decision to be made, what is the chance event, and what is the consequence for this problem? How many decision alternatives are there? How many outcomes are there for the chance event? b. Suppose that management of Myrtle Air Express believes that the probability of strong demand is .7 and the probability of weak demand is .3. Use the expected value approach to determine an optimal decision. c. Suppose that the probability of strong demand is .8 and the probability of weak demand is .2. What is the optimal decision using the expected value approach?

A real estate investor has the opportunity to purchase land currently zoned residential. If the county board approves a request to rezone the property as commercial within the next year, the investor will be able to lease the land to a large discount firm that wants to open a new store on the property. However, if the zoning change is not approved, the investor will have to sell the property at a loss. Profits (in thousands of dollars) are shown in the following payoff table.

$$\begin{matrix} \text{ } & \text{State} & \text{of Nature}\\ \text{ } & \text{Rezoning Approved} & \text{Rezoning Not Approved}\\ \text{Decision Alternative} & \text{s1} & \text{s2}\\ \text{Purchase, d1} & \text{600} & \text{-200}\\ \text{Do not purchase, d2} & \text{0} & \text{0}\\ \end{matrix}$$

a. If the probability that the rezoning will be approved is .5, what decision is recommended? What is the expected profit? b. The investor can purchase an option to buy the land. Under the option, the investor maintains the rights to purchase the land anytime during the next three months while learning more about possible resistance to the rezoning proposal from area residents. Probabilities are as follows.

$$\begin{aligned} \text { Let } & H = \text { high resistance to rezoning } \\ L & = \text { low resistance to rezoning } \end{aligned}$$

$$P ( H ) = .55 \quad P \left( s _ { 1 } | H \right) = .18 \quad P \left( s _ { 2 } | H \right) = .82$$

$$P ( L ) = .45 \quad P \left( s _ { 1 } | L \right) = .89 \quad P \left( s _ { 2 } | L \right) = .11$$

What is the optimal decision strategy if the investor uses the option period to learn more about the resistance from area residents before making the purchase decision? c. If the option will cost the investor an additional $10,000, should the investor purchase the option? Why or why not? What is the maximum that the investor should be willing to pay for the option?

Hudson Corporation is considering three options for managing its data processing operation: continue with its own staff, hire an outside vendor to do the managing (referred to as outsourcing), or use a combination of its own staff and an outside vendor. The cost of the operation depends on future demand. The annual cost of each option (in thousands of dollars) depends on demand as follows.

$$\begin{matrix} \text{ } & \text{ } & \text{Demand}\\ \text{Staffing Options} & \text{High} & \text{Medium} & \text{Low}\\ \text{Own staff} & \text{650} & \text{650} & \text{600}\\ \text{Outside vendor} & \text{900} & \text{600} & \text{300}\\ \text{Combination} & \text{800} & \text{650} & \text{500}\\ \end{matrix}$$

a. If the demand probabilities are .2, .5, and .3, which decision alternative will minimize the expected cost of the data processing operation? What is the expected annual cost associated with your recommendation? b. What is the expected value of perfect information?

"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."

"Myrtle Air Express decided to offer direct service from Cleveland to Myrtle Beach. Management must decide between a full-price service using the company’s new fleet of jet aircraft and a discount service using smaller-capacity commuter planes. It is clear that the best choice depends on the market reaction to the service Myrtle Air offers. Management developed estimates of the contribution to profit for each type of service based on two possible levels of demand for service to Myrtle Beach: strong and weak. The following table shows the estimated quarterly profits (in thousands of dollars):

$$\begin{aligned} &\text { Demand for Service }\\ &\begin{array}{lcr} \text { Service } & \text { Strong } & \text { Weak } \\ \text { Full Price } & \$ 960 & -\$ 490 \\ \text { Discount } & \$ 670 & \$ 320 \end{array} \end{aligned}$$

Suppose that management of Myrtle Air Express believes that the probability of strong demand is 0.7 and the probability of weak demand is 0.3. Use the expected value approach to determine an optimal decision."

A regional telephone company operates three identical relay stations at different locations. During a one-year period, the number of malfunctions reported by each station and the causes are shown below.

$$\begin{matrix} \text{Station}& A & B & C\\ \hline \text{ Problems with electricity supplied} & 2 & 1& 1\\ \text{Computer malfunction} & 4 & 3 & 2\\ \text{ Malfunctioning electrical equipment} & 5& 4& 2\\ \text{ Caused by other human errors} & 7& 7& 5 \end{matrix}$$

Suppose that a malfunction was reported and it was found to be caused by other human errors. What is the probability that it came from station C?

What was the purpose of the Seneca Falls Convention?

A stock's returns have the following distribution:

$$\small{ \begin{array}{lcc} \begin{array}{l} \textbf{ Demand for the } \\ \textbf{ Company's Products } \end{array} & \begin{array}{c} \textbf{ Probability of This } \\ \textbf{ Demand Occurring } \end{array} & \begin{array}{c} \textbf{ Rate of Retum if This } \\ \textbf{ Demand Occurs } \end{array} \\ \hline \text { Weak } & 0.1 & (50 \%) \\ \text { Below average } & 0.2 & (5) \\ \text { Average } & 0.4 & 16 \\ \text { Above average } & 0.2 & 25 \\ \text { Strong } & \underline{0.1} & 60\\ &\underline{\underline{0.1}}\\\ \end{array}}$$

Calculate the stock's expected return, standard deviation, and coefficient of variation.

Demand function. Given the demand function

$$p=D(x)=\frac{1,000}{x}$$

find the average price (in dollars) over the demand interval $[400, 600]$.

Hale’s TV Productions is considering producing a pilot for a comedy series in the hope of selling it to a major television network. The network may decide to reject the series, but it may also decide to purchase the rights to the series for either one or two years. At this point in time, Hale may either produce the pilot and wait for the network’s decision or transfer the rights for the pilot and series to a competitor for $100,000. Hale’s decision alternatives and profits (in thousands of dollars) are as follows:

$$\begin{matrix} \text{ } & \text{ } & \text{State of Nature}\\ \text{Decision Alternative} & \text{Reject, s1} & \text{1 Year, s2} & \text{2 Years, s3}\\ \hline \text{Produce pilot, d1} & \text{-100} & \text{50} & \text{150}\\ \text{Sell to competitor, d2} & \text{100} & \text{100} & \text{100}\\ \end{matrix}$$

The probabilities for the states of nature are $P \left( s _ { 1 } \right) = .2 , P \left( s _ { 2 } \right) = .3 ,$ and $P \left( s _ { 3 } \right) = .5$. For a consulting fee of

$$5000, an agency will review the plans for the comedy series and indicate the overall chances of a favorable network reaction to the series. Assume that the agency review will result in a favorable (F) or an unfavorable (U) review and that the following probabilities are relevant. \begin{array} { l l l } { P ( F ) = .69 } & { P \left( s _ { 1 } | F \right) = .09 } & { P \left( s _ { 1 } | U \right) = .45 } \\ { P ( U ) = .31 } & { P \left( s _ { 2 } | F \right) = .26 } & { P \left( s _ { 2 } | U \right) = .39 } \\ { } & { P \left( s _ { 3 } | F \right) = 65 } & { P \left( s _ { 3 } | U \right) = .16 } \end{array} a. Construct a decision tree for this problem. b. What is the recommended decision if the agency opinion is not used? What is the expected value? c. What is the expected value of perfect information? d. What is Hale’s optimal decision strategy assuming the agency’s information is used? e. What is the expected value of the agency’s information? f. Is the agency’s information worth the$$

5000 fee? What is the maximum that Hale should be willing to pay for the information? g. What is the recommended decision?

The distance from Potsdam to larger markets and limited air service have hindered the town in attracting new industry. Air Express, a major overnight delivery service, is considering establishing a regional distribution center in Potsdam. But Air Express will not establish the center unless the length of the runway at the local airport is increased. Another candidate for new development is Diagnostic Research, Inc. (DRI), a leading producer of medical testing equipment. DRI is considering building a new manufacturing plant. Increasing the length of the runway is not a requirement for DRI, but the planning commission feels that doing so will help convince DRI to locate their new plant in Potsdam. Assuming that the town lengthens the runway, the Potsdam planning commission believes that the probabilities shown in the following table are applicable.

$$\begin{matrix} \text{ } & \text{DRI Plant} & \text{No DRI Plant}\\ \text{Air Express Center} & \text{.30} & \text{.10}\\ \text{No Air Express Center} & \text{.40} & \text{.20}\\ \end{matrix}$$

For instance, the probability that Air Express will establish a distribution center and DRI will build a plant is .30. The estimated annual revenue to the town, after deducting the cost of lengthening the runway, is as follows:

$$\begin{matrix} \text{ } & \text{DRI Plant} & \text{No DRI Plant}\\ \text{Air Express Center} & \text{\$600,000} & \text{\$150,000}\\ \text{No Air Express Center} & \text{\$250,000} & \text{-\$200,000}\\ \end{matrix}$$

If the runway expansion project is not conducted, the planning commission assesses the probability DRI will locate their new plant in Potsdam at .6; in this case, the estimated annual revenue to the town will be $450,000. If the runway expansion project is not conducted and DRI does not locate in Potsdam, the annual revenue will be$0 since no cost will have been incurred and no revenues will be forthcoming. a. What is the decision to be made, what is the chance event, and what is the consequence? b. Compute the expected annual revenue associated with the decision alternative to lengthen the runway. c. Compute the expected annual revenue associated with the decision alternative to not lengthen the runway. d. Should the town elect to lengthen the runway? Explain. e. Suppose that the probabilities associated with lengthening the runway were as follows:

$$\begin{matrix} \text{ } & \text{DRI Plant} & \text{No DRI Plant}\\ \text{Air Express Center} & \text{.40} & \text{.10}\\ \text{No Air Express Center} & \text{.30} & \text{.20}\\ \end{matrix}$$

What effect, if any, would this change in the probabilities have on the recommended decision?