Question

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:

Investment Weather Conditions

Shortage Stable Supply Surplus

Motel $-7,500 $12,000 $23,000

Restaurant 3000 7,000 6,500

Theater 5000 6,000 4,000

Determine the best investment, using the following decision criteria.

a. Maximax

b. Maximin

c. Minimax regret

d. Hurwicz (α = 0.4)

e. Equal likelihood

to be done in excel

Answer 1

a. Max of motel = 23,000, max of restaurant = 7000, max of theatre = 6000

   max(23,000 , 7000, 6000) = 23000

best investment usig maximax is motel.

b. min of motel = 7500, min of restaurant = 3000, min of theatre = 4000

max( 7500 , 3000, 4000) =4000

best investment using maximin is theatre.

c. Max of motel = 23,000, max of restaurant = 7000, max of theatre = 6000

min ( 23000 , 7000 , 6000) = 6000

best investment using minimax is theatre.

d. Hurwicz= a(min value)+ (1-a) max value

Hurwicz for motel = (0.4*-7500)+(0.6*23000) = 16800

Hurwicz for restaurant = (0.4*3000)+(0.6*7000) = 5400

Hurwicz for theatre = (0.4*4000)+(0.6*6000) = 5200

best investment using hurwicz is theatre.

e. equal likelihood:

Mean cost of motel = 27,500

Mean cost of restaurant = 5500

Mean cost of theatre = 5000

best investment using equal likelihod is theatre.