Zhu Manufacturing is considering the introduction of a family of new products. Long-term demand for the product group is somewhat predictable, so the manufacturer must be concerned with the risk of choosing a process that is inappropriate. Faye Zhu is VP of operations. She can choose among batch manufacturing or custom manufacturing, or she can invest in group technology. Faye won't be able to forecast demand accurately until after she makes the process choice. Demand will be classified into four compartments: poor, fair, good, and excellent. The table below indicates the payoffs (profits) associated with each process/demand combination, as well as the probabilities of each long-term demand level:

	POOR	FAIR	GOOD	EXCELLENT
Probability	$.1$	$.4$	$.3$	$.2$
Batch	$\$200,000$	$\$1,000,000$	$\$1,200,000$	$\$1,300,000$
Custom	$\$100,000$	$\$300,000$	$\$700,000$	$\$800,000$
Group technology	$-\$1,000,000$	$-\$500,000$	$\$500,000$	$\$2,000,000$

What would Faye Zhu be willing to pay for a forecast that would accurately determine the level of demand in the future?

Leah Johnson, director of Urgent Care of Brookline, wants to increase capacity to provide low-cost flu shots but must decide whether to do so by hiring another full-time nurse or by using part-time nurses. The table below shows the expected costs of the two options for three possible demand levels:

Using expected value, what should Ms. Johnson do?

Jerry Bildery's factory is considering three approaches for meeting an expected increase in demand. These three approaches are increasing capacity, using overtime, and buying more equipment. Demand will increase either slightly $(S)$, moderately $(\mathrm{M})$, or greatly $(\mathrm{G})$. The profits for each approach under each possible scenario are as follows:

Since the goal is to maximize, and Jerry is risk-neutral, he decides to use the equally likely decision criterion to make the decision as to which approach to use. According to this criterion, which approach should be used?

Howard Weiss, Inc., is considering building a sensitive new radiation scanning device. His managers believe that there is a probability of $0.4$ that the ATR $\mathrm{Co}$. will come out with a competitive product. If Weiss adds an assembly line for the product and ATR Co. does not follow with a competitive product, Weiss's expected profit is $\$ 40,000$; if Weiss adds an assembly line and ATR follows suit, Weiss still expects $\$ 10,000$ profit. If Weiss adds a new plant addition and ATR does not produce a competitive product, Weiss expects a profit of $\$ 600,000$; if ATR does compete for this market, Weiss expects a loss of $\$ 100,000$.

Compute the expected value of perfect information.

Given the following conditional value table, determine the appropriate decision under uncertainty using maximax.

Andrew Thomas, a sandwich vendor at Hard Rock Cafe's annual Rockfest, created a table of conditional values for the various alternatives (stocking decision) and states of nature (size of crowd):

The probabilities associated with the states of nature are $0.3$ for a big demand, $0.5$ for an average demand, and $0.2$ for a small demand.

Compute the expected value of perfect information (EVPI).

Even though independent gasoline stations have been having a difficult time, Ian Langella has been thinking about starting his own independent gasoline station. Ian's problem is to decide how large his station should be. The annual returns will depend on both the size of his station and a number of marketing factors related to the oil industry and demand for gasoline. After a careful analysis, Ian developed the following table:

For example, if Ian constructs a small station and the market is good, he will realize a profit of $\$ 50,000$.

What is the maximin decision?

Even though independent gasoline stations have been having a difficult time, Ian Langella has been thinking about starting his own independent gasoline station. Ian's problem is to decide how large his station should be. The annual returns will depend on both the size of his station and a number of marketing factors related to the oil industry and demand for gasoline. After a careful analysis, Ian developed the following table:

For example, if Ian constructs a small station and the market is good, he will realize a profit of $\$ 50,000$.

What is the maximax decision?

Deborah Kellogg buys Breathalyzer test sets for the Winter Park Police Department. The quality of the test sets from her two suppliers is indicated in the following table:

For example, the probability of getting a batch of tests that are $1\%$ defective from Winter Park Technology is .70. Because Kellogg orders $10,000$ tests per order, this would mean that there is a 70 probability of getting 100 defective tests out of the $10,000$ tests if Winter Park Technology is used to fill the order. A defective Breathalyzer test set can be repaired for $\$0.50$. Although the quality of the test sets of the second supplier, Dayton Enterprises, is lower, it will sell an order of $10,000$ test sets for $\$ 37$ less than Winter Park.

Develop a decision tree.

Jeffrey Helm owns a health and fitness center called Bulk-Up in Harrisburg. He is considering adding more floor space to meet increasing demand. He will either add no floor space $(\mathrm{N})$, a moderate area of floor space $(\mathrm{M})$, a large area of floor space (L), or an area of floor space that doubles the size of the facility (D). Demand will either stay fixed, increase slightly, or increase greatly. The following are the changes in Bulk-Up's annual profits under each combination of expansion level and demand change level:

Jeffrey is risk averse and wishes to use the maximin criterion.

What are his decision alternatives and what are the states of nature?

Leah Johnson, director of Urgent Care of Brookline, wants to increase capacity to provide low-cost flu shots but must decide whether to do so by hiring another full-time nurse or by using part-time nurses. The table below shows the expected costs of the two options for three possible demand levels:

Draw an appropriate decision tree showing payoffs and probabilities.

Peggy Lane Corp., a producer of machine tools, wants to move to a larger site. Two alternative locations have been identified: Bonham and McKinney. Bonham would have fixed costs of $800,000 per year and variable costs of$14,000 per standard unit produced. McKinney would have annual fixed costs of $920,000 and variable costs of$13,000 per standard unit. The finished items sell for $29,000 each. What is the relevance of break-even points for these cities?

What are the four requirements of a linear programming problem?

Howard Weiss, Inc., is considering building a sensitive new radiation scanning device. His managers believe that there is a probability of $0.4$ that the ATR $\mathrm{Co}$. will come out with a competitive product. If Weiss adds an assembly line for the product and ATR Co. does not follow with a competitive product, Weiss's expected profit is $\$ 40,000$; if Weiss adds an assembly line and ATR follows suit, Weiss still expects $\$ 10,000$ profit. If Weiss adds a new plant addition and ATR does not produce a competitive product, Weiss expects a profit of $\$ 600,000$; if ATR does compete for this market, Weiss expects a loss of $\$ 100,000$.

Determine the EMV of each decision.