Page 764, Problem 4
Problem Statement:
The Nitro Fertilizer Company is developing a new fertilizer. If Nitro markets the product
and it is successful, the company will earn a $50,000 profit; if it is unsuccessful, the
company will lose $35,000. In the past, similar products have been successful 60% of the
time. At a cost of $5000, the effectiveness of the new fertilizer can be tested. If the test
result is favorable, there is an 80% chance that the fertilizer will be successful. If the test
result is unfavorable, there is only a 30% chance that the fertilizer will be successful.
There is a 60% chance of a favorable test result and a 40% chance of an unfavorable test
result.
a) Draw a decision tree and perform fold back manually.
b) Solve the problem using WinQSB. (two styles are used)
Notice that the decision tree developed for manual calculation and the decision tree
developed to be used for WinQSB look different. While they are both correct, they
represent different tree styles. The first decision tree has three branches from the first
decision node, while the second tree has two branches from the first decision node
followed by another decision node with two branches. The combination of these two
decision nodes in the second tree is the same logic as the three branches of the first tree.
Notice a name is given to each node for WinQSB to distinguish nodes. However, these
names could have been unique to ease later analysis of the output.
1
Draw a decision tree and perform fold back manually.
PAGE 764-PROBLEM#4
$16k
$50k
successful $50k (0.60)
unsuccessful -$35k (0.4)
-$35K
$45k
$28k
market
market
$16k
unsuccessful -$35(.2)
-$40k
$14.8k
do not market -$5k
Favorable result(.6)
1
successful $50k (.8)
$28k
-$5k
do test -$5000
-$14.5k
$45k
successful $50k (.3)
unfavorable
result(0.4)
$-5k
do not market $0
unsuccessful -$35 (.7)
market
-$40k
do not market -$5k
-$5k
$0
decision
events
final earn
2
Solve the problem using WinQSB.
A decision tree is drawn before entering data into the software. This tree is somehow
different from the one above. For this decision tree the style of your textbook is used,
that is terminal values are summation of all value along their path.
3
Input:
4
Output (solution) from WinQSB:
5
For this decision tree the style of WinQSB textbook is used, that is each value is
considered exactly on the branch that it happens.
Below is input and output for WinQSB. Compare with the previous one and notice the
differences.
6
Input:
7
Output:
8