This document presents two problems demonstrating decision-making models. The first problem shows a situation where probabilities cannot be assigned to future outcomes, involving an investment choice. The second problem demonstrates expected value analysis by estimating probabilities of different game scenarios and determining the best play for a football team based on yardage expectations. Both problems provide examples of quantitative decision analysis techniques.

1. Term
Project
MBA 550
Decision
Support
Systems
1

2. Introduction
People make decisions all the time.
Sometimes we choose to do things without even
knowing why we did it. In business, however,
decisions have to be well calculated as this determines
whether the business will survive. Decision-making
models are a structured way of making decisions. A
decision-making situation includes several
components-the decision themselves and the actual
events that may occur in the future. At the time a
decision is made, the decision maker is uncertain
which states of nature will occur in the future and has
no control over them.

3. Introduction (cont.)
Several decision-making techniques are available to
aid the decision maker in dealing with this type of
decision situation in which there is certainty or
uncertainty.
Decision situation can be categorized into two classes:
a. Situations in which probabilities cannot be
assigned to future occurrences.
b. Situations in which probabilities can be
assigned.
This project is about Decision-Making Models.
First we will explain the problems, provide solutions ,
and evaluate the project.

4. MBA 550
Team Project
PROBLEM #1
PROBABILITY FOR EACH ECONOMIC
CONDITIONS (GOOD AND BAD)
(situations in which probabilities cannot be assigned to
future occurrences)
PROBLEM#2
EXPECTED VALUE OF PERFECT INFORMATION
AND DETERMINE THE BEST PROJECT
(situations in which probabilities can be assigned)

5. Problem # 1
An investor must decide between two alternative
investments-stocks and bonds. The return for each
investment, given two future economic conditions, is shown
in the following payoff table:
____________________________________
Economic Conditions
Investments Good Bad
Stocks $10,000 $-4,000
Bonds 7,000 2,000
What probability for each economic condition would make
the investor indifferent to the choice between stocks and
bonds?

6. Answer
To make investor indifference:
Let x1 = good probability and
x2 = bad probability
The probabilities are unknown, but you want the
expected values of choosing either stocks or
bonds to be the same, then:
(10000)x1 + (-4000)x2 = (7000)x1 + (2000)x2
And where x1 + x2 = 1, or x2 = 1 – x1
Stocks = bonds

7. Answer (cont.)
Substituting for x2 = (1 – x1)
(10000)x1 + [(-4000)(1 – x1)] = (7000)x1 + [(2000)(1-x1)]
Multiplying this out:
(10000)x1 – 4000 + (4000)x1 = (7000)x1 + 2000- 2000x1
Combining whole numbers and multiples of x1
(9)x1 = 6
Then x1=6/9 = .67 (there is rounding in this fraction;
rounding fractional solutions will results in suboptimal
solutions (not the optimal solutions).

8. Answer (cont.)
x1 = good conditions probability = .67
X2 = bad conditions probability = (1-x1) = (1-.67) = .33
.67 ($10000) + .33 ($-4000) = .67 ($7000) = (1- .67) = .33
Notice due to “rounding off” to the nearest conditions
probabilities, the solutions resulted in suboptimal not
optimal solutions.
Stocks 6700 + (-1320) = 5380
Bonds 4690 +e 660 = 5350

9. Problem # 2
DEFENSE
Wide
Play 54 63 Tackle Nickel Blitz
Off tackle 3 -2 9 7 -1
Option -1 8 -2 9 12
Toss sweep 6 16 -5 3 14
Draw -2 4 3 10 -3
Pass 8 20 12 -7 -8
Screen -5 -2 8 3 16

10. Problem # 2 (cont.)

11. Answer
DEFENSE
Wide
54 63 Tackle Nickel Blitz
probability (a) 0.4 0.1 0.2 0.2 0.1
Off Tackle 3 -2 9 7 -1
Option -1 8 -2 9 12
Toss Sweep 6 16 -5 3 14
Draw -2 4 3 10 -3
Pass 8 20 12 -7 -8
Screen -5 -2 8 3 16
probablility (b) 0.1 0.1 0.1 0.1 0.6

12. Answer (cont.)
weighted
yds/play a) best to worst ranking
4.1 pass 1 5.4
3 toss sweep 2 5
5 off tackle 3 4.1
1.9 option 4 3
5.4 draw 5 1.9
1.6 screen 6 1.6
1.1 b) Toss sweep
8.6
10.4
-0.3
-1.5
10

13. Evaluation
In this term project, we examined and learned two
decision models. Problem number one is a situation
in which an investor needs to decide between two
alternative investments- stock and bonds. This is a
situation in which probabilities cannot be assigned to
future occurrences. We don’t know what’s the
economic conditions is going to be. It’s either good or
bad economic conditions. Since the probabilities are
unknown, we want the expected values of choosing
either stocks or bonds to be the same. In real
situations, however, model parameters are frequently
uncertain because they reflect the future as well as the
present, and future conditions are rarely known with
certainty. We also found out that “rounding off”
fractions can result in a suboptimal solutions.

14. Evaluation (cont.)
In problem number two, we apply the concept of
expected value as a decision-making criterions.
We first estimate the probability of occurrence of
each state of nature. Once the estimate have
been determined, the expected value for each
decision alternative can be computed. In our
problem, the Tech has the game data of the State,
and reviewed the probabilities that State will use
each of its defense. Tech coaches was able to
determined what play should they run, if they
have the third down and has 10 yards away from
the goal line.

15. References
Taylor, B. (2010) Introduction to Management
Science, New Jersey. Prentice Hall