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MAT540 Homework Week 2 Page 1 of 4 Chapter 12
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MAT540 Homework Week 2 Page 1 of 4MAT540
Week 2 Homework
Chapter 12
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:
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.
Best of the best =Motel 23,000, Restaurant 7000, Theater 6000
a. Maximax = 23,000
Best of the maximin =Motel -7500, Rest. 3000, Theatre 4000
b. Maximin = 4,000
Shortage = 5000-(-7500) = 12,500, 5000-3000 = 2000, 5000-5000 = 0
Stable Supply 12,000-12,000 = 0, 12,000-7000 = 5000, 12,000-6000 = 6000
Surplus 23,000-23,000 = 0, 23000-6500 = 16,500, 23,000-4000=19,000
Subtract the best maximum from each row: 23,000-12,000-5000 = 6000
c. Minimax regret = 6000
Take the best of the best and the worst of the best in each column
The Hurwicz (a = 0.4) the alpha must total 1
.4 x23000 + .6 x -7500 (MOTEL)
=9200 + -4500
= 4,700
.4 x 7000 + .6 x 3000 (REST)
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, = 2800 + 1800
= 4,600
.4 x 6000 = .6 x 4000 (THEATER)
= 2400 + 2400
= 4800
The best investment is the theater
d. Hurwicz (α = 0.4) = 4800
Next add all rows and divide by 3
Motel -7500+12,000+23,000/3= 9,166.67
Restaurant 3000+7000+6500/3=5,500
Theatre 5000+6000+4000/3=5,000
e. Equal likelihood = 9,1667.67
Best Investment is the Theatre
2. A concessions manager at the Tech versus A&M football game must decide whether to have the
vendors sell sun visors or umbrellas. There is a 35% chance of rain, a 25% chance of overcast skies, and a
40% chance of sunshine, according to the weather forecast in college junction, where the game is to be
held. The manager estimates that the following profits will result from each decision, given each set of
weather conditions:
MAT540 Homework Week 2 Page 2 of 4
Decision
Weather Conditions
Rain 0.35
Overcast 0.25
Sunshine 0.40 Sun visors $-400 $-200 $1,500 Umbrellas 2,100 0 -800
a. Compute the expected value for each decision and select the best one.
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