"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?"

"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.

Suppose that the probabilities that Amy drives 12,000, 15,000, and 18,000 miles per year are 0.5, 0.4, and 0.1, respectively. What option should Amy choose using the expected value approach?"

Does the price of an appliance convey something about its quality? Forty-eight different dishwashers were ranked on characteristics ranging from an overall satisfaction score, washing ($x_1$), energy use ($x_2$), noise ($x_3$), ease of use ($x_4$), and cycle time (in minutes). The Bosch (SHE55M1[2]UC) had the highest performance score of 82 while the GE (GLD4408R[WW]) had the lowest at 53. Ratings pictograms were converted to numerical values for $x_1$, ..., $x_4$, where 5=Excellent, 4=Very good, 3=Good, 2=Fair and 1=Poor. Use a statistical computer package to explore the relationship between various pairs of variables in the table.

'Model','Price','Score','x1','x2','x3','x4','Cycle_time' 'Amana ADB1600AW[W]',350,61,4,4,2,3,130 'Asko D3531',1600,80,4,5,5,4,145 'Asko D5233XXL[HS]',1500,56,,4,4,4,180 'Asko D5253XXL',1300,77,5,4,4,4,180 'Bosch SHE55M1[2]UC',850,82,5,5,4,4,120 'Bosch SHE6AP0[2]UC',600,75,5,4,3,4,135 'Bosch SHX43P1[2]UC',800,77,5,5,3,4,115 'Bosch SHX45P0[5]UC',900,79,5,5,4,4,115 'Bosch SHX65P0[5]UC',1150,75,4,4,4,4,120 'Bosch SHX6AP0[2]UC',700,77,5,5,4,4,110 'Bosch SHX98M0[9]UC',1550,82,5,4,5,4,115 'Dacor Epicure ED24[S]',1550,69,4,4,4,3,110 'Electrolux Wave-Touch',1200,65,4,4,4,5,135 'Frigidaire Gallery [1]',350,70,5,3,3,3,155 'Frigidaire Gallery [2]',380,68,4,4,3,4,145 'Frigidaire Gallery [3]',500,66,4,4,3,4,135 'GE GDWF100R[WW]',600,70,5,4,3,4,120 'GE GLD4408R[WW]',400,53,3,4,2,3,135 'GE GLD7400R[WW]',600,62,4,4,3,5,110 'GE Profile PDWT500R[WW]',1300,77,5,4,4,5,110 'Hotpoint HDA3600R[WW]',300,53,3,5,1,2,115 'Jenn-Air JDB3200AW[W]',1100,64,4,5,4,3,125 'Kenmore 1318[2]',840,79,5,5,4,4,145 'Kenmore 1324[2]',410,58,3,4,3,3,125 'Kenmore 1344[2]',300,60,4,3,2,3,110 'Kenmore 1348[2]',500,77,5,4,3,3,120 'Kenmore 1374[2]',650,80,5,4,3,4,125 'Kenmore 1389[2]',500,78,5,4,3,4,135 'Kenmore Elite UltraWash [1]',780,79,5,5,4,4,140 'Kenmore Elite UltraWash [2]',1100,81,5,5,4,4,145 'Kenmore Pro 1317[3]',1280,79,5,5,5,4,145 'KitchenAid KUDE50CV[SS]',1200,76,5,5,4,4,125 'KitchenAid KUDE60FV[WH]',1340,78,5,5,4,4,135 'KitchenAid KUDE70CV[SS]',1300,81,5,5,5,4,140 'KitchenAid KUDS30IV[WH]',675,77,5,4,3,4,120 'KitchenAid KUDS40CV[WH]',990,79,5,4,4,4,115 'LG LDF6920[WW]',700,79,5,4,4,4,125 'LG Steam LDF7932[ST]',1000,81,5,4,4,5,130 'Maytag MDB7609AW[W]',450,75,5,4,3,2,120 'Maytag MDB8959AW[W]',750,71,4,4,3,5,120 'Maytag MTB4709AW[W]',400,69,5,4,2,3,125 'Miele Inspira G2142SC[WH]',1150,76,5,5,4,3,145 'Whirlpool DU1030XTX[Q]',350,68,5,4,2,3,130 'Whirlpool DU1055XTV[Q]',400,76,5,4,3,3,125 'Whirlpool DU1300XTV[Q]',420,72,5,3,3,3,140 'Whirlpool Gold GU2300XTV[Q]',550,78,5,4,3,4,135 'Whirlpool Gold GU2800XTV[Q]',700,77,5,5,3,4,155 'Whirlpool Gold GU3600XTV[Q]',800,77,4,5,4,4,145

Look at the variables Price, Score, and Cycle Time individually. What can you say about symmetry? About outliers.

"Southland Corporation’s decision to produce a new line of recreational products resulted in the need to construct either a small plant or a large plant. The best selection of plant size depends on how the marketplace reacts to the new product line. To conduct an analysis, marketing management has decided to view the possible long-run demand as low, medium, or high. The following payoff table shows the projected profit in millions of dollars:

$$\begin{array}{lccc} \text { Plant Size } & \text { Low } & \text { Medium } & \text { High } \\ \text { Small } & 150 & 200 & 200 \\ \text { Large } & 50 & 200 & 500 \end{array}$$

Recommend a decision based on the use of the optimistic, conservative, and minimax regret approaches."

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.

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 permile basis. The monthly lease cost, the mileage allowance, and the cost for additional miles are as follows:

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

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. What is the decision, and what is the chance event?

"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.

Suppose that, after further consideration, Amy concludes that the probabilities that she will drive 12,000, 15,000, and 18,000 miles per year are 0.3, 0.4, and 0.3, respectively. What decision should Amy make using the expected value approach?"

What is a risk profile? Explain the risk profiles with regard to oil prices for an oil producer and a gasoline retailer.

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

$$\begin{matrix} \text{ } & \text{States} & \text{of} & \text{Nature}\\ \hline \text{Decision Alternative} & \text{s1} & \text{s2} & \text{s3}\\ \text{d1} & \text{250} & \text{100} & \text{25}\\ \text{d2} & \text{100} & \text{100} & \text{75}\\ \end{matrix}$$

a. Construct a decision tree for this problem. b. Suppose that the decision maker obtains the probabilities $P \left( s _ { 1 } \right) = .65 , P \left( s _ { 2 } \right) = .15$, and $P \left( s _ { 3 } \right) = .20$

Use the expected value approach to determine the optimal decision.

Southland Corporation’s decision to produce a new line of recreational products resulted in the need to construct either a small plant or a large plant. The best selection of plant size depends on how the marketplace reacts to the new product line. To conduct an analysis, marketing management has decided to view the possible long-run demand as low, medium, or high. The following payoff table shows the projected profit in millions of dollars:

$$\begin{array}{lccc} \text { Plant Size } & \text { Low } & \text { Medium } & \text { High } \\ \text { Small } & 150 & 200 & 200 \\ \text { Large } & 50 & 200 & 500 \end{array}$$

Construct a decision tree.

"Southland Corporation’s decision to produce a new line of recreational products resulted in the need to construct either a small plant or a large plant. The best selection of plant size depends on how the marketplace reacts to the new product line. To conduct an analysis, marketing management has decided to view the possible long-run demand as low, medium, or high. The following payoff table shows the projected profit in millions of dollars:

$$\begin{array}{lccc} \text { Plant Size } & \text { Low } & \text { Medium } & \text { High } \\ \text { Small } & 150 & 200 & 200 \\ \text { Large } & 50 & 200 & 500 \end{array}$$

What is the decision to be made, and what is the chance event for Southland’s problem?"

using the information presented in the table in Exercise $5.15$, calculate the following probabilities:

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

$$\begin{aligned} &\text { Decision Alternative }\\ &\begin{array}{lrl} d_1 & 10 & 1 \\ d_2 & 4 & 3 \end{array} \end{aligned}$$

Perform sensitivity analysis on the payoffs for decision alternative $d_1$. Assume the probabilities are as given in part a, and find the range of payoffs under states of nature $s_1$ and $s_2$ that will keep the solution found in part a optimal. Is the solution more sensitive to the payoff under state of nature $s_1$ or $s_2$ ?"

You compare two strings s1 and s2 using ________.

a. (s1==s2)

b. s1.compare(s2)

c. compareTo(s1, s2)

d. s1.compareTo(s2)