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:

SIZE OF FIRST STATION	GOOD MARKET (S)	FAIR MARKET (S)	POOR MARKET (S)
Small	$50,000$	$20,000$	$-10,000$
Medium	$80,000$	$\$30,000$	$-20,000$
Large	$100,000$	$30,000$	$-40,000$
Very large	$300,000$	$25,000$	$-160,000$

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 $\$ 50,000$.

Develop a decision table for this decision, like the one illustrated in Table A. 2 earlier.

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

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.

Louisiana is busy designing new lottery scratchoff games. In the latest game, Bayou Boondoggle, the player is instructed to scratch off one spot: $A, B$, or $C$. A can reveal "Loser," "Win $\$1$," or "Win $\$ 50$. "B can reveal "Loser" or "Take a Second Chance." C can reveal "Loser" or "Win $\$ 500$." On the second chance, the player is instructed to scratch off D or E. D can reveal "Loser" or "Win $\$1$." E can reveal "Loser" or "Win $\$10$." The probabilities at A are .9, .09, and .01. The probabilities at $\mathrm{B}$ are $.8$ and $.2$. The probabilities at $\mathrm{C}$ are $.999$ and $.001$. The probabilities at $\mathrm{D}$ are $.5$ and $.5$. Finally, the probabilities at $\mathrm{E}$ are Use proper symbols and label all branches clearly. Calculate the expected value of this game.

In Exercise 19.34, what strategy would the company select if it were using the maximin criterion? The maximax criterion? The minimax regret criterion?

Southeastern Oklahoma State University's business program has the facilities and faculty to handle an enrollment of 2,000 new students per semester. However, in an effort to limit class sizes to a "reasonable" level (under 200, generally), Southeastern's dean, Holly Lutze, placed a ceiling on enrollment of 1,500 new students. Although there was ample demand for business courses last semester, conflicting schedules allowed only 1,450 new students to take business courses. What are the utilization and efficiency of this system?

The S&OP team at Kansas Furniture, has received the following estimates of demand requirements:

a) Assuming one-time stock out costs for lost sales of $\$ 100$ per unit, inventory carrying costs of $\$ 25$ per unit per month, and zero beginning and ending inventory, evaluate these two plans on an incremental cost basis:

• Plan A: Produce at a steady rate (equal to minimum requirements) of $1,000$ units per month and subcontract additional units at a $\$ 60$ per unit premium cost.

• Plan B: Vary the workforce, to produce the prior month's demand. The firm produced $I,300$ units in June. The cost of hiring additional workers is $\$ 3,000$ per 100 units produced. The cost of layoffs is $\$ 6,000$ per 100 units cut back.

Note: Both hiring and layoff costs are incurred in the month of the change, (i.e. going from production of $1,300$ in July to $1,000$ in August requires a layoff (and related costs) of 300 units in August, just as going from production of $1,000$ in August to $1,200$ in September requires hiring (and related costs) of 200 units in September).

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

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

A television network is deciding whether or not to give its newest television show a spot during prime viewing time at night. For this to happen, it will have to move one of Page 353 its most viewed shows to another slot. The network conducts a survey asking its viewers which show they would rather watch. The network will keep its current lineup of shows unless the majority of the customers want to watch the new show. The network receives 827 responses, of which 428 indicate that they would like to see the new show in the lineup.

a. Set up the hypotheses to test if the television network should give its newest television show a spot during prime viewing time at night.

b. Calculate the value of the test statistic and the $p$-value.

c. At $\alpha=0.01$, what should the television network do?

Ken Gilbert owns the Knoxville Warriors, a minor league baseball team in Tennessee. He wishes to move the Warriors south, to either Mobile (Alabama) or Jackson (Mississippi). The table below gives the factors that Gilbert thinks are important, their weights, and the scores for Mobile and Jackson.

Which site should he select?

The following table gives the map coordinates and the shipping loads for a set of cities that we wish to connect through a central hub.

If the shipments from city A triple, how does this change the coordinates?

The following is a table of activities associated with a project at Rafay Ishfaq's software firm in Chicago, their durations, and what activities each must precede:

Define the critical path, listing all critical activities in chronological order.