qat1task5
Task 5
A. Expected Value For The Four Decision Branches
After closely examining the expected value for each of the four decision branches below it is clear to see that Outcome Node #1 (new product, thorough development) has the highest total value, at $210,200, across the range of uncertain market outcomes. This is from summing the predicted gains as modified their differential probabilities.
#1 New Product, Thorough Development
P
Mkt Reaction
Predicted Gains
VALUE
0.4
Good
$500,000
$200,000
0.4
Moderate
$25,000
$10,000
0.2
Poor
$1,000
$200
TOTAL
$210,200
#2 New Product, Rapid Development
P
Mkt Reaction
Predicted Gains
VALUE
0.1
Good
$500,000
$50,000
0.2
Moderate
$25,000
$5,000
0.7
Poor
$1,000
$700
TOTAL
$55,700
#3 Consolidate, Strengthen Product
P
Mkt Reaction
Predicted Gains
VALUE
0.3
Good
$200,000
$60,000
0.4
Moderate
$10,000
$4,000
0.3
Poor
$3,000
$900
TOTAL
$64,900
#4 Consolidate, Reap Without Investing
P
Mkt Reaction
Predicted Gains
VALUE
0.6
Moderate
$10,000
$6,000
0.4
Poor
$1,000
$400
TOTAL
$6,400
B. How The Determination was Reached
The dollar outcomes and probabilities that make up the contingency table are subjected to decision tree analysis so as to visualize all probable results. In the first place, the four alternative outcomes are made to form the main branches, or nodes, of the decision tree. Then the conditional probabilities for each node are calculated.
We can take Outcome Node #1 as an example. Firstly, we input the probabilities of 0.4, 0.4 and 0.2 for “good”, “moderate” and “poor” market reception. We then proceed to develop the marginal, conditional, and joint probabilities for each terminal end-point. The formula for the conditional probability of events A and B is changed as:
P(A ∩ B) = P(B) P(A | B)
By developing the likely revenue of market response outcome and summing the results, we obtain the expected
A. Expected Value For The Four Decision Branches
After closely examining the expected value for each of the four decision branches below it is clear to see that Outcome Node #1 (new product, thorough development) has the highest total value, at $210,200, across the range of uncertain market outcomes. This is from summing the predicted gains as modified their differential probabilities.
#1 New Product, Thorough Development
P
Mkt Reaction
Predicted Gains
VALUE
0.4
Good
$500,000
$200,000
0.4
Moderate
$25,000
$10,000
0.2
Poor
$1,000
$200
TOTAL
$210,200
#2 New Product, Rapid Development
P
Mkt Reaction
Predicted Gains
VALUE
0.1
Good
$500,000
$50,000
0.2
Moderate
$25,000
$5,000
0.7
Poor
$1,000
$700
TOTAL
$55,700
#3 Consolidate, Strengthen Product
P
Mkt Reaction
Predicted Gains
VALUE
0.3
Good
$200,000
$60,000
0.4
Moderate
$10,000
$4,000
0.3
Poor
$3,000
$900
TOTAL
$64,900
#4 Consolidate, Reap Without Investing
P
Mkt Reaction
Predicted Gains
VALUE
0.6
Moderate
$10,000
$6,000
0.4
Poor
$1,000
$400
TOTAL
$6,400
B. How The Determination was Reached
The dollar outcomes and probabilities that make up the contingency table are subjected to decision tree analysis so as to visualize all probable results. In the first place, the four alternative outcomes are made to form the main branches, or nodes, of the decision tree. Then the conditional probabilities for each node are calculated.
We can take Outcome Node #1 as an example. Firstly, we input the probabilities of 0.4, 0.4 and 0.2 for “good”, “moderate” and “poor” market reception. We then proceed to develop the marginal, conditional, and joint probabilities for each terminal end-point. The formula for the conditional probability of events A and B is changed as:
P(A ∩ B) = P(B) P(A | B)
By developing the likely revenue of market response outcome and summing the results, we obtain the expected