Exam (elaborations)
MAT540 Homework Week 2 Page 1 of 4 Chapter 12
- Course
- Institution
MAT540 Homework Week 2 Page 1 of 4 Chapter 12 MAT 540 Homework Week 2 Page 1 of 4 Chapter 12
[Show more]
Seller
Follow
solutions
Reviews received
Content preview
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)
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/
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller solutions. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $7.49. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
78998 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now