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).

	Demand for Service
Service	Strong	Weak
Full price	$960	-$490
Discount	$670	$320

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

"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):

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

If nothing is known about the probabilities of the chance outcomes, what is the recommended decision using the optimistic, conservative, and minimax regret approaches?"

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:

$$\begin{aligned} &\text { Long-Run Demand }\\ &\begin{array}{lccc} \text { Plan Size } & \text { Low } & \text { Medium } & \text { High } \\ \text { Small } & 150 & 200 & 200 \\ \text { Large } & 50 & 200 & 500 \end{array} \end{aligned}$$

Recommend a decision based on the use of 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 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):

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

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?"

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?

"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 the probability of strong demand is 0.8 and the probability of weak demand is 0.2. What is the optimal decision using the expected value approach?"

Consumer Reports conducted a taste test on 19 brands of boxed chocolates. The following data show the price per serving, based on the FDA serving size of 1.4 ounces, and the quality rating for the 19 chocolates tested (Consumer Reports, February 2002).

$$\begin{matrix} \text{Manufacturer} & \text{Price} & \text{Rating}\\ \text{Bernard Callebaut} & \text{3.17} & \text{Very Good}\\ \text{Candinas} & \text{3.58} & \text{Excellent}\\ \text{Fannie May} & \text{1.49} & \text{Good}\\ \text{Godiva} & \text{2.91} & \text{Very Good}\\ \text{Hershey’s} & \text{0.76} & \text{Good}\\ \text{L.A. Burdick} & \text{3.70} & \text{Very Good}\\ \text{La Maison du Chocolate} & \text{5.08} & \text{Excellent}\\ \text{Leonidas} & \text{2.11} & \text{Very Good}\\ \text{Lindt} & \text{2.20} & \text{Good}\\ \text{Martine’s} & \text{4.76} & \text{Excellent}\\ \text{Michael Recchiuti} & \text{7.05} & \text{Very Good}\\ \text{Neuchatel} & \text{3.36} & \text{Good}\\ \text{Neuchatel Sugar Free} & \text{3.22} & \text{Good}\\ \text{Richard Donnelly} & \text{6.55} & \text{Very Good}\\ \text{Russell Stover} & \text{0.70} & \text{Good}\\ \text{See’s} & \text{1.06} & \text{Very Good}\\ \text{Teuscher Lake of Zurich} & \text{4.66} & \text{Very Good}\\ \text{Whitman’s} & \text{0.70} & \text{Fair}\\ \text{Whitman’s Sugar Free} & \text{1.21} & \text{Fair}\\ \end{matrix}$$

Suppose that you would like to determine whether products that cost more rate higher in quality. For the purpose of this exercise, use the following binary dependent variable:

$$y = 1\text{ if the quality rating is very good or excellent and 0 if good or fair}$$

a. Write the logistic regression equation relating x  price per serving to y. b. Use Minitab to compute the estimated logit. c. Use the estimated logit computed in part (b) to compute an estimate of the probability a chocolate that has a price per serving of $4.00 will have a quality rating of very good or excellent. d. What is the estimate of the odds ratio? What is its interpretation?

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?

Over the past few years the percentage of students who leave Lakeland College at the end of the first year has increased. Last year Lakeland started a voluntary one-week orientation program to help first-year students adjust to campus life. If Lakeland is able to show that the orientation program has a positive effect on retention, they will consider making the program a requirement for all first-year students. Lakeland’s administration also suspects that students with lower GPAs have a higher probability of leaving Lakeland at the end of the first year. In order to investigate the relation of these variables to retention, Lakeland selected a random sample of 100 students from last year’s entering class. The data are contained in the data set named Lakeland; a portion of the data follows.

The dependent variable was coded as y = 1 if the student returned to Lakeland for the sophomore year and y = 0 if not. The two independent variables are:

$x_1$ = GPA at the end of the first semester

$x_2$ = 0 if the student did not attend the orientation program,

$x_2$ = 1 if the student attended the orientation program

a. Write the logistic regression equation relating $x_1$ and $x_2$ to y.

b. What is the interpretation of E( y) when $x_2$ = 0?

c. Use both independent variables and Minitab to compute the estimated logit.

d. Conduct a test for overall significance using $\alpha$ = .05.

e. Use $\alpha$ = .05 to determine whether each of the independent variables is significant.

f. Use the estimated logit computed in part (c ) to estimate the probability that students with a 2.5 grade point average who did not attend the orientation program will return to Lakeland for their sophomore year. What is the estimated probability for students with a 2.5 grade point average who attended the orientation program?

g. What is the estimated odds ratio for the orientation program? Interpret it.

h. Would you recommend making the orientation program a required activity? Why or why not?

An amusement park reports an increase of 21 bungee customers from Saturday to Sunday. If this represents an increase of $7 \%$ in the number of customers:

a. What would a $1 \%$ increase be?

b. What would a $10 \%$ increase be?

c. What would a $5.1 \%$ increase be?

d. What was the original number of customers?

Consider the following logistic regression equation:

$$\text{ln(Estimated odds ratio)} = 0.1 + 0.5X_{1i} + 0.2X_{2i}$$

a. Interpret the meaning of the logistic regression coefficients.

The Lake Placid Town Council has decided to build a new community center to be used for conventions, concerts, and other public events, but considerable controversy surrounds the appropriate size. Many influential citizens want a large center that would be a showcase for the area, but the mayor feels that if demand does not support such a center, the community will lose a large amount of money. To provide structure for the decision process, the council narrowed the building alternatives to three sizes: small, medium, and large. Everybody agreed that the critical factor in choosing the best size is the number of people who will want to use the new facility. A regional planning consultant provided demand estimates under three scenarios: worst case, base case, and best case. The worst-case scenario corresponds to a situation in which tourism drops significantly; the base-case scenario corresponds to a situation in which Lake Placid continues to attract visitors at current levels; and the best-case scenario corresponds to a significant increase in tourism. The consultant has provided probability assessments of .10, .60, and .30 for the worst-case, base-case, and best-case scenarios, respectively. The town council suggested using net cash flow over a five-year planning horizon as the criterion for deciding on the best size. A consultant developed the following projections of net cash flow (in thousands of dollars) for a five-year planning horizon. All costs, including the consultant’s fee, are included.

a. What decision should Lake Placid make using the expected value approach?

b. Compute the expected value of perfect information. Do you think it would be worth trying to obtain additional information concerning which scenario is likely to occur?

c. Suppose the probability of the worst-case scenario increases to .2, the probability of the base-case scenario decreases to .5, and the probability of the best-case scenario remains at .3. What effect, if any, would these changes have on the decision recommendation?

d. The consultant suggested that an expenditure of $\$150,000$ on a promotional campaign over the planning horizon will effectively reduce the probability of the worst-case scenario to zero. If the campaign can be expected to also increase the probability of the best-case scenario to .4, is it a good investment

What is the molar mass of PDC?