In a city there is a plan to build an airport. There are two alternate locations for the airport
Project 7 Math 102
Project 7 Math 102
You are given the probability table below.
|
|
B |
|
|
|
A |
0.204 |
0.476 |
0.68 |
|
|
0.006 |
0.314 |
0.32 |
|
|
0.21 |
0.79 |
1 |
If P(B|A) =0.3 and P(B|)=0.02, what are these probabilities:
P(|A) = P(A)/P(A) = 0.476/0.68 = 0.7
P(|) =P()/P() = = 0.314/0.32= 0.98125
P(B)= 0.21
P()= 0.79
P(A|B) = P(AB) /P(B) = 0.204/0.21 = 0.97
P(|B)= P(B)/P(B) = 0.006/0.21=0.02857
P(A|)=P(A)/P()= 0.476/0.79=0.6
P(|)=P()/P()=0.314/0.79 = 0.40
In a city there is a plan to build an airport. There are two alternate locations for the airport. An investor is planning to build a hotel at one of these locations. Depending on the selected location of the airport the present value (PV) of the hotel will vary. The investor would like to also evaluate the options of buying both locations or not investing in any of these locations at all. The following table provides the total cost and the PV for each location.
|
|
Location 1 |
Location 2 |
|
Total Cost of Land, Construction, etc |
$18* |
$12 |
|
PV of hotel if airport is built here |
$31 |
$23 |
|
PV of hotel if airport is built at the other location |
$6 |
$4 |
*Millions of Dollars
Fill in the values in the payoff table and apply different decision rules to come up with a recommendation.
· The Pessimistic Rule: ___________
· The Optimistic Rule: ___________
· A Compromise Rule (Use alpha=0.3): ___________
· The Average Rule: ___________
· The Regret Avoidance Rule: ___________
_____________________
Payoff Table
|
|
Airport at Location 1 |
Airport at Location 2 |
|
Build a hotel at Location 1 |
13 |
-12 |
|
Build a hotel at Location 2 |
-8 |
11 |
|
Buying both locations |
5 |
-1 |
|
Not investing in any of these locations at all |
0 |
0 |
Based on the sensitivity analysis in the table above, chose a value of alpha such that the option “build at both location” gives the highest profit.
Alpha = 0.
Page 1 of 5
Page 1 of 5
Page 3 of 3
Sensitivity with Respect to Alpha
-15
-10
-5
0
5
10
15
Alpha
Profit (x $Millions)
Build a hotel at Location 1
1310.585.530.5-2-4.5-7-9.5-12
Build a hotel at Location 2
119.17.25.33.41.5-0.4-2.3-4.2-6.1-8
Build at both Location
54.43.83.22.621.40.80.2-0.4-1
Not investing in any
Locations
00000000000
00.10.20.30.40.50.60.70.80.91