1.A local real estate investor in Orlando is considering three alternative inves

Question

1.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 Stable Supply $15,000 6,000 Surplus $20,000 6,000 5,000 Investment Shortage Motel Restaurant Theater S-8,000 2,000 6,000 8,000 OM3020 Homework Assignments (1-9) Determine the best investment, using the following decision criteria a. Maximax b. Maximin C. Minimax regret d. Hurwicz (a-.4) e. Equal likelihood f. Assume the probabilities for the gasoline shortage, stable supply and surplus are .5,.3 and .2 compute the expect value (payoff) of each investment option, the expected opportunity loss of each investment option, and the expect value of perfect information. Based on the expected value or expected opportunity loss, decide the best investment option

Explanation / Answer

a)

Maximax: here the maximum payoff is selected, that maximizes the total payoff.

Here, the maximum payoff is 20000. This payoff or income comes from Motel when there is surplus gasoline available. Hence we select this option under maximax.

b)

Maximin we select that alternative which maximizes the minimum payoff.

For motel, minimum payoff is = -8000

for  restaurant minimum payoff is = 2000

for theater minimum payoff = 5000

Hence since we are trying to maximize the minimum payoff, we select 5000, since this is the maximum of the three options.

Hence we select theater for maximin

c) The minimax regret strategy is the one that minimises the maximum regret.

here we find the largest payoff for each option, then subtract the all the numbers from the largest one for that option.

Motel, highest payoff is 20000. regret for shortage of gasoline = 20000 - (-8000) = 28000

similarly we do this for all option of theater and restaurant.

the regrets are given in the following table:

maximum regret for motel is 28000

maximum regret for restaurant is 6000

maximum regret for theater is 1000.

we minimize this regret, hence we choose theater since minimum regret is 1000.

d) here we take a tolerance for risk given as alpha = 0.4

the maximum payoff of each option is multiplied with alpha, the minum payoff is multiplied with (1-alpha). both are then added to the find the value. the highest among the 3 options will be chosen.

Motel:

highest = 20000, 20000*0.4 = 8000

smallest = -8000, -8000*0.6 = -4800

total for motel = 8000 - 4800 = 3200

Restaurant:

highest = 8000*0.4 = 3200

smallest = 2000*0.6 = 1200

total for restaurant = 3200 + 1200 = 4400

Theater:

highest = 6000*0.4 = 2400

smallest = 5000*0.6 = 3000

total for theater = 2400 + 3000 = 5400

Hence highest among them is 5400 for theater, hence choose option theater.

investment shortage stable supply surplus Motel 28000 5000 0 Restaurant 6000 0 2000 Theater 0 0 1000

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