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# Decision: Maximax, Maximin, Hurwicz, Equal Likelihood

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1. The owner of the Burger Doodle Restaurant is considering two ways to expand operations: open a drive up window or serve breakfast. The increase in profits resulting from these proposed expansions depends on whether a competitor opens a franchise down the street. The possible profits from each expansion in operations, given both future competitive situations, are shown in the following payoff table:

Competitor
Decision Open Not Open
Drive-up window \$-6,000 \$20,000
Breakfast 4,000 8,000

Select the best decision, using the following decision criteria.
a. Maximax
b. Maximin

2. The Oakland Bombers professional basketball team just missed making the playoffs last season and believes it needs to sign only one very good free agent to make the playoffs next season. The team is considering four players: Barry Bond, Rayneal O'Neil, Marvin Johnson, and Michael Gordon. Each player differs according to position, ability, and attractiveness to fans. The payoffs (in \$1,000,0000s) to the team for each player, based on the contract, profits from attendance, and team product sales for several different season outcomes, are provided in the following table:
Season Outcome
Player Loser Competitive Makes Playoffs
Byrd \$-3.2 \$ 1.3 4.4
O'Neil -5.1 1.8 6.3
Johnson -2.7 0.7 5.8
Gordon -6.3 -1.6 9.6

Determine the best decision, using the following decision criteria.
a. Maximax
b. Maximin
c. Hurwicz (&#945; = .60)
d. Equal likelihood

https://brainmass.com/statistics/quantative-analysis-of-data/260090

#### Solution Preview

The answers are in the attached file:
1 The owner of the Burger Doodle Restaurant is considering two ways to expand operations: open a drive up window or serve breakfast. The increase in profits resulting from these proposed expansions depends on whether a competitor opens a franchise down the street. The possible profits from each expansion in operations, given both future competitive situations, are shown in the following payoff table:
Competitor
Decision Open Not Open
Drive-up window (\$6,000) \$20,000
Breakfast 4,000 8,000

Select the best decision, using the following decision criteria.
a. Maximax
b. Maximin

a. Maximax

Maximax strives to maximize profits by choosing the option with the highest return. It is the 'optimist's choice'.
Competitor Maximum
Decision Open Not Open Maximum of the row
Drive-up window (\$6,000) \$20,000 \$20,000
Breakfast ...

#### Solution Summary

Decisions have been made for the given payoffs using Maximax, Maximin, Hurwicz, and Equal Likelihood criteria.

\$2.19

## Decision Analysis using the criteria like Maximax, Maximin, Minimax, Hurwicz, Equal likelihood

Please provide a detailed step by step solution to the given problems.

Problem 2:
The owner of the Burger Doodle Restaurant is considering two ways to expand operations: open a drive-up window or serve breakfast. The increase in profits resulting from these proposed expansions depends on whether a competitor opens a franchise down the street. The possible profits from each expansion in operations, given both future competitive situations, are shown in the following payoff table:

Competitor

Decision Open Not Open

Drive-up window \$ - 6,000 \$20,000
Breakfast 4,000 8,000

Select the best decision, using the following decision criteria.
a. Maximax
b. Maximin

Problem 4:
Brooke Bentley, a student in business administration, is trying to decide which management science course to take next quarter - I, II, or III. "Steamboat" Fulton, "Death" Ray, and "Sadistic" Scott are the three management science professors who teach the courses. Brooke does not know who will teach what course. Brooke can expect a different grade in each of the courses, depending on who teaches it next quarter, as shown in the following payoff table:

Professor

Course Fulton Ray Scott

I B D D
II C B F
III F A C

Determine the best course to take next quarter, using the following criteria.
a. Maximax
b. Maximin

Problem 6:
A company must decide now which of three products to make next year to plan and order proper materials. The cost per unit of producing each product will be determined by whether a new union labor contract passes or fails. The cost per unit for each product, given each contract result is shown in the following payoff table:

Contract Outcome

Product Pass Fail

1 \$7.50 \$6.00
2 4.00 7.00
3 6.50 3.00

Determine which product should be produced, using the following decision criteria.
a. Maximax
b. Maximin

Problem 8:
A local real estate investor in Orlando is considering three alternative investments: a motel, a restaurant, or a theater. Profits from the motel or restaurant will be affected by the availability of gasoline and the number of tourists: profits from the theater will be relatively stable under any conditions. The following payoff table shows the profit or loss that could result from each investment:

Gasoline Availability

Investment Shortage Stable Supply Surplus

Motel \$ - 8,000 \$15,000 \$20,000
Restaurant 2,000 8,000 6,000
Theater 6,000 6,000 5,000

Determine the best investment, using the following decision criteria.
a. Maximax
b. Maximin
c. Minimax regret
d. Hurwicz (a = .4)
e. Equal likelihood

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