Myrtle Air Express decided to offer direct service from Cleveland to Myrtle Beach. Management must decide between a fullprice 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):

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

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?

"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?"

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.

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?

"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:

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

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?"

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?

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:

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?

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.

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.

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?

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?

Contact your local Chamber of Commerce. (The Chamber of Commerce collects information about local businesses, and most of its services are free.) Ask for the information you desire.

The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year’s program. Advertising alternatives include television, radio, and newspaper. Audience estimates, costs, and maximum media usage limitations are as shown:

$$\begin{array}{lcrr} \text { Constraint } & \text { Television } & \text { Radio } & \text { Newspaper } \\ \text { Audience per advertisement } & 100,000 & 18,000 & 40,000 \\ \text { Cost per advertisement } & \$ 2,000 & \$ 300 & \$ 600 \\ \text { Maximum media usage } & 10 & 20 & 10 \end{array}$$

To ensure a balanced use of advertising media, radio advertisements must not exceed 50 percent of the total number of advertisements authorized. In addition, television should account for at least 10 percent of the total number of advertisements authorized.

If the promotional budget is limited to $18,200, how many commercial messages should be run on each medium to maximize total audience contact? What is the allocation of the budget among the three media, and what is the total audience reached?

"The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year’s program. Advertising alternatives include television, radio, and newspaper. Audience estimates, costs, and maximum media usage limitations are as shown:

$$\begin{array}{lcrr} \text { Constraint } & \text { Television } & \text { Radio } & \text { Newspaper } \\ \text { Audience per advertisement } & 100,000 & 18,000 & 40,000 \\ \text { Cost per advertisement } & \$ 2,000 & \$ 300 & \$ 600 \\ \text { Maximum media usage } & 10 & 20 & 10 \end{array}$$

To ensure a balanced use of advertising media, radio advertisements must not exceed 50 percent of the total number of advertisements authorized. In addition, television should account for at least 10 percent of the total number of advertisements authorized.

By how much would audience contact increase if an extra $100 were allocated to the promotional budget?"