MAT540 Homework Week 2 Page 1 of 4 MAT540 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)
This study source was downloaded by 100000840946462 from CourseHero.com on 02-15-2022 11:43:53 GMT -06:00
https://www.coursehero.com/file/14469629/MAT540-Homework-Week-2-Page-1-of-4/
= 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.
This study source was downloaded by 100000840946462 from CourseHero.com on 02-15-2022 11:43:53 GMT -06:00
https://www.coursehero.com/file/14469629/MAT540-Homework-Week-2-Page-1-of-4/
Rain (SV) 0.35 x -400 = -140, (UMB) 0.35 x .2100 = 735 Overcast (SV) 0.25 x -200 = -50 (UMB) 0.25 x 0 = 0 Sunshine (SV) 0.40 x 1500 – 600 (UMB) 0.40 x -800 = -160 The best is umbrellas at 735. b. Develop the opportunity loss table and compute the expected opportunity loss for each decision. Rain
Overcast
Sunshine
Visors
2100-(-400) = 2500
0-(-200) = 200
1500-1500 = 0
Umbrellas
2100-2100 = 0
0-0=0
1500-(-800) = 2300
Regret Loss Table Visors
2500
200
0
Umbrellas
0
0
2300
Expected loss = use probabilities Visor = 3.5(2500 + .25(200) + .40(0) = 925 Umbrella = 3.5(0) + .25(0) + .40(2300) = 920 Best minimum is to sell umbrellas (920) 3. Place-Plus, 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 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 in the following payoff table. Place-Plus real estate development firm has hired an economist to assign a probability to each direction interest rates may take over the
This study source was downloaded by 100000840946462 from CourseHero.com on 02-15-2022 11:43:53 GMT -06:00
https://www.coursehero.com/file/14469629/MAT540-Homework-Week-2-Page-1-of-4/
next 5 years. The economist has determined that there is a 0.45 probability that interest rates will decline, a 0.35 probability that rates will remain stable, and a 0.2 probability that rates will increase. a. Using expected value, determine the best project. Expected Value Interest Rate Decline
Stable
Increase
.45
.35
.2
Off Park$0.4
$1.55
$3.5 = .45(0.4)+.35(.55)+.2(3.5) = 1.4225
Off Building
2.5
1.8
2.75= .45(2.5)+.35(1.8)+.2(2.75) = 2.305
Warehouse
1.7
1.45
1.5 = .4(1.7)+.35(1.45)+.2(1.5) = 1.5725
Mall
0.8
2.3
3.5= .45(0.8)+.35(2.3)+.2(3.5) = 1.865
Condos
3.2
1.5
0.5 = .45(3.2)+.35(1.5)+.2(0.5) = 2.065
The best project is the office building at $2.305 million EVwoPI= expect value 2.305 b. Determine the expected value of perfect information. Evpi=EVwPI-VwPI = 2.305 Million .45 Off Park$0.4
.35 $1.55
.2 $3.
Off Building
2.5
1.8
2.75
Warehouse
1.7
1.45
1.5 = .45(3.2)+.35(2.3)+.2(3.5) = 2.945
Mall
0.8
2.3
3.5
Condos
3.2
1.5
0.5
Evpi=EVwPI-EVwoPI EVpi – 2,945-2.305 = .64 Million
This study source was downloaded by 100000840946462 from CourseHero.com on 02-15-2022 11:43:53 GMT -06:00
https://www.coursehero.com/file/14469629/MAT540-Homework-Week-2-Page-1-of-4/
4. The director of career advising at Orange Community College wants to use decision analysis to provide information to help students decide which 2-year degree program they should pursue. The director has set up the following payoff table for six of the most popular and successful degree programs at OCC that shows the estimated 5-Year gross income ($) from each degree for four future economic conditions: Degree Program Economic Conditions Recession Average Good Robust
Best
Best/Worse
Graphic design
150,000
175,000
220,000
200,000
220,000
150,000
Nursing
160,000
180,000
205,000
215,000
215,000
160,000
Real estate
125,000
165,000
220,000
210,000
220,000
125,000
Medical technology
135,000
180,000
210,000
270,000
270,000
135,000
Culinary technology
110,000
145,000
235,000
205,000
235,000
110,000
Comp Info techn
130,000 150,000
190,000
245,000
245,000
130,000
Maximax = 270,000 Medical Technology Minimax = 160,000 Nursing Conditions Recession Average Good Robust Graphic design
150,000 + 175,000+ +220,000 + 200,000 = 745,000/3 = 248,333.33
Nursing
160,000 + 180,000
+205,000 + 215,000 = 760,000/3 = 253,333.32
Real estate
125,000 + 165,000
+220,000 + 210,000 = 720,000/3 = 240,000.00
Medical technology
135,000
180,000
210,000
270,000 = 795,000/3 = 265,000.00
Culinary technology
110,000
145,000
235,000
205,000 = 695,000/3 = 231,666.67
Comp Info techn
130,000 150,000
190,000
245,000 = 715,000/3 = 238,333.33
Equal likelihood = 265,000.00 Medical Technology Hurwicz 189,000 Medical Technology
Best
Best/Worse
This study source was downloaded by 100000840946462 from CourseHero.com on 02-15-2022 11:43:53 GMT -06:00
https://www.coursehero.com/file/14469629/MAT540-Homework-Week-2-Page-1-of-4/