Exam 5: Advanced Linear Programming Applications

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​Revenue management methodology enables an airline to maximize the number of full-fare seats it sells on each flight.

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Shown below is the solution to the linear program for finding Player A's optimal mixed strategy in a two-person, zero-sum game. Shown below is the solution to the linear program for finding Player A's optimal mixed strategy in a two-person, zero-sum game.    a.What is Player A's optimal mixed strategy? b.What is Player B's optimal mixed strategy? c.What is Player A's expected gain? d.What is Player B's expected loss? a.What is Player A's optimal mixed strategy? b.What is Player B's optimal mixed strategy? c.What is Player A's expected gain? d.What is Player B's expected loss?

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​List several types of organizations with multiple operating units where data envelopment analysis might be applied and give examples of possible inputs and outputs for each organization.

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Consider a two-person, zero-sum game where the payoffs listed below are the winnings for Company X. Identify the pure strategy solution. What is the value of the game? Consider a two-person, zero-sum game where the payoffs listed below are the winnings for Company X. Identify the pure strategy solution. What is the value of the game?

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​Revenue management methodology enables an airline to

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Consider the following two-person, zero-sum game. Payoffs are the winnings for Company X. Formulate the linear program that determines the optimal mixed strategy for Company X. ​ Consider the following two-person, zero-sum game. Payoffs are the winnings for Company X. Formulate the linear program that determines the optimal mixed strategy for Company X. ​

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The analysis of a two-person, zero-sum game begins with checking to see whether a pure strategy exists.

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The output shows the solution to a DEA model where facilities in Seaview (S), Farmington (F), Lewiston (L), and San Domingo (D) are compared. The inputs, in order, are number of machines, size of work force, and goodness of location. The outputs, in order, are production, quality rating, and on-time completion percentage. The model examines the efficiency of Lewiston. MIN 0S+0F+0L+0D+1E S.T. 1) 1S+1F+1L+1D=1 2) 5S+22F+36L+15D−36E<0 3) 400S+1500F+3150L+1060D−3150E<0 4) 24S+13F+32L+17D−32E<0 5) 800S+2900F+1860L+1700D+0E>1860 6) 95S+92F+83L+94D+0E>83 7) 83S+85F+90L+91D+0E>90 OPTIMAL SOLUTION Objective Function Value = 0.510 The output shows the solution to a DEA model where facilities in Seaview (S), Farmington (F), Lewiston (L), and San Domingo (D) are compared. The inputs, in order, are number of machines, size of work force, and goodness of location. The outputs, in order, are production, quality rating, and on-time completion percentage. The model examines the efficiency of Lewiston. MIN 0S+0F+0L+0D+1E S.T. 1) 1S+1F+1L+1D=1 2) 5S+22F+36L+15D−36E<0 3) 400S+1500F+3150L+1060D−3150E<0 4) 24S+13F+32L+17D−32E<0 5) 800S+2900F+1860L+1700D+0E>1860 6) 95S+92F+83L+94D+0E>83 7) 83S+85F+90L+91D+0E>90 OPTIMAL SOLUTION Objective Function Value = 0.510      a.Is the Lewiston plant efficient? Why or why not? If not, which plants should it emulate in order to improve? b.How much more production does the composite facility provide than the Lewiston site? c.What is the quality rating for the composite facility? The output shows the solution to a DEA model where facilities in Seaview (S), Farmington (F), Lewiston (L), and San Domingo (D) are compared. The inputs, in order, are number of machines, size of work force, and goodness of location. The outputs, in order, are production, quality rating, and on-time completion percentage. The model examines the efficiency of Lewiston. MIN 0S+0F+0L+0D+1E S.T. 1) 1S+1F+1L+1D=1 2) 5S+22F+36L+15D−36E<0 3) 400S+1500F+3150L+1060D−3150E<0 4) 24S+13F+32L+17D−32E<0 5) 800S+2900F+1860L+1700D+0E>1860 6) 95S+92F+83L+94D+0E>83 7) 83S+85F+90L+91D+0E>90 OPTIMAL SOLUTION Objective Function Value = 0.510      a.Is the Lewiston plant efficient? Why or why not? If not, which plants should it emulate in order to improve? b.How much more production does the composite facility provide than the Lewiston site? c.What is the quality rating for the composite facility? a.Is the Lewiston plant efficient? Why or why not? If not, which plants should it emulate in order to improve? b.How much more production does the composite facility provide than the Lewiston site? c.What is the quality rating for the composite facility?

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​Explain the differences between the LP formulations for a conservative portfolio and moderate-risk portfolio.

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Revenue management methodology was originally developed for

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Consider a two-person, zero-sum game where the payoffs listed below are the winnings for Player A. Identify the pure strategy solution. What is the value of the game? ​ Consider a two-person, zero-sum game where the payoffs listed below are the winnings for Player A. Identify the pure strategy solution. What is the value of the game? ​   ​

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The Eastern Washington County School Corporation is interested in comparing educational performance at four elementary schools and has hired you to prepare a DEA model to do so. After detailed conversations with the corporation administrative staff and the building principals, you have isolated the following input and output measurements: The Eastern Washington County School Corporation is interested in comparing educational performance at four elementary schools and has hired you to prepare a DEA model to do so. After detailed conversations with the corporation administrative staff and the building principals, you have isolated the following input and output measurements:   Data is collected for each school on each measure   Develop the DEA model that would evaluate the efficiency of Ralston Elementary School. Data is collected for each school on each measure The Eastern Washington County School Corporation is interested in comparing educational performance at four elementary schools and has hired you to prepare a DEA model to do so. After detailed conversations with the corporation administrative staff and the building principals, you have isolated the following input and output measurements:   Data is collected for each school on each measure   Develop the DEA model that would evaluate the efficiency of Ralston Elementary School. Develop the DEA model that would evaluate the efficiency of Ralston Elementary School.

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To develop a portfolio that provides the best return possible with a minimum risk, the linear programming model will have an objective function which

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Revenue management methodology can be applied in the case of nonperishable assets.

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The goal of portfolio models is to create a portfolio that provides the best balance between risk and return.

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​Write a summary of the DEA approach and explain how you would interpret the solution.

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If a pure strategy solution exists for a two-person, zero-sum game, it is the optimal solution to the game.

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Portfolio manager Max Gaines needs to develop an investment portfolio for his clients who are willing to accept a moderate amount of risk. His task is to determine the proportion of the portfolio to invest in each of the five mutual funds listed below so that the portfolio provides an annual return of no less than 3%. Formulate the appropriate linear program. ​​ Portfolio manager Max Gaines needs to develop an investment portfolio for his clients who are willing to accept a moderate amount of risk. His task is to determine the proportion of the portfolio to invest in each of the five mutual funds listed below so that the portfolio provides an annual return of no less than 3%. Formulate the appropriate linear program. ​​

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Revenue management methodology was originally developed for the banking industry.

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In portfolio models, risk is minimized by diversification.

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