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A real estate development firm is considering several alternative development projects. These include building and leasing an office park, purchasing a parcel of land and building an office building to rent, buying and leasing a warehouse, building a strip mall, and building and selling condominiums. The financial success of these projects depends on interest rate movement in the next 5 years. The various development projects and their 5-year financial return (in $1,000,000s) given that interest rates will decline, remain stable, or increase, are shown in the following payoff table:interest rateproject decline stable increaseoffice park $0.50 $1.70 $4.50office building 1.5 1.9 2.5warehouse 1.7 1.4 1mall 0.7 2.4 3.6condominiums 3.2 1.5 0.6 Flag question: Question 4Question 4Tips2.25 ptsDetermine the best investment option using the Hurwicz criteria with 𝛼=0.3.Group of answer choicesmallcondominiumswarehouseoffice buildingoffice park Flag question: Question 5Question 5Tips2.25 ptsDetermine the best investment option using the maximin decision criteria.Group of answer choicesoffice buildingmallwarehousecondominiumsoffice park

Question

A real estate development firm is considering several alternative development projects. These include building and leasing an office park, purchasing a parcel of land and building an office building to rent, buying and leasing a warehouse, building a strip mall, and building and selling condominiums. The financial success of these projects depends on interest rate movement in the next 5 years. The various development projects and their 5-year financial return (in 1,000,000s)giventhatinterestrateswilldecline,remainstable,orincrease,areshowninthefollowingpayofftable:interestrateprojectdeclinestableincreaseofficepark1,000,000s) given that interest rates will decline, remain stable, or increase, are shown in the following payoff table:interest rateproject decline stable increaseoffice park 0.50 1.701.70 4.50office building 1.5 1.9 2.5warehouse 1.7 1.4 1mall 0.7 2.4 3.6condominiums 3.2 1.5 0.6 Flag question: Question 4Question 4Tips2.25 ptsDetermine the best investment option using the Hurwicz criteria with 𝛼=0.3.Group of answer choicesmallcondominiumswarehouseoffice buildingoffice park Flag question: Question 5Question 5Tips2.25 ptsDetermine the best investment option using the maximin decision criteria.Group of answer choicesoffice buildingmallwarehousecondominiumsoffice park

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Solution

Question 4:

The Hurwicz criterion is a decision-making criterion that is a compromise between the maximin and maximax criteria. It is defined by a coefficient of realism, 𝛼, which reflects the decision-maker's optimism.

Here's how to calculate it:

  1. For each project, calculate the weighted average of the best (maximum) and worst (minimum) payoffs. The weights are given by the coefficient of realism, 𝛼, and 1-𝛼. The formula is: Hurwicz value = 𝛼 * (best payoff) + (1-𝛼) * (worst payoff).

  2. Choose the project with the highest Hurwicz value.

Let's calculate:

Office Park: 0.3 * 4.5 + 0.7 * 0.5 = 1.7 Office Building: 0.3 * 2.5 + 0.7 * 1.5 = 1.8 Warehouse: 0.3 * 1.7 + 0.7 * 1 = 1.21 Mall: 0.3 * 3.6 + 0.7 * 0.7 = 1.47 Condominiums: 0.3 * 3.2 + 0.7 * 0.6 = 1.38

So, according to the Hurwicz criterion with 𝛼=0.3, the best investment option is the Office Building.

Question 5:

The maximin decision criterion involves choosing the decision with the highest minimum payoff.

Let's find the minimum payoff for each project:

Office Park: min(0.5, 1.7, 4.5) = 0.5 Office Building: min(1.5, 1.9, 2.5) = 1.5 Warehouse: min(1.7, 1.4, 1) = 1 Mall: min(0.7, 2.4, 3.6) = 0.7 Condominiums: min(3.2, 1.5, 0.6) = 0.6

So, according to the maximin decision criterion, the best investment option is the Office Building.

This problem has been solved

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