DecisionTreePrimer 4

CHAPTER 4

Solutions for Exercises

4.1 Chapter 1 Exercise Solutions

Exercise 1.1. Arthrodax Company
i) Figure 4.1 shows the decision tree. ii) As the decision tree shows, the preferred alternative is to accept the order and purchase the injection molder, with an expected pro¯ t of $154.4 thousand.
Exercise 1.2. Arthrodax Company (con't)
i) Figure 4.2 shows the decision tree. ii) As the decision tree shows, the preferred alternative is to accept the order and purchase the cases, with an expected pro¯ t of $99.9 thousand.
Exercise 1.3. Arthrodax Company (con't)
i) Figure 4.3 shows the decision tree. Note that in addition to the alternatives shown in this decision tree, it would be possible to immediately purchase the injection molder, or to immediately reject the purchase of the injection molder, without waiting to determine how many units will be ordered. These alternatives are shown in Figure 4.2 for the preceding exercise. Of course, these alternatives cannot be more preferred than the alternative of waiting to see how many units are ordered, since it costs nothing to wait, and you gain further information by waiting. ii) As the decision tree shows, the preferred strategy is to accept the order, and if Ranger orders 100 units then purchase the molder while if Ranger orders 50 units purchase the cases. The expected pro¯ t for this strategy is $102.1 thousand.
Exercise 1.4. Aba Manufacturing
i) This would potentially avoid the second $250,000 setup cost. ii) Figure 4.4 shows the decision tree for this part. iii) From the decision tree, we see that the preferred alternative is to manufacture all 200,000 PC boards now.

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CHAPTER 4 SOLUTIONS FOR EXERCISES

Fixed
Cost

Molder
Variable
Successful?
Cost
Yes

Revenue

$208

$500

$252

$500

$252

$500

(0.6)
Purchase Molder

$120

Purchase Cases

No

$100

Reject Ranger Offer

Figure 4.1

$148
$0

Units
Purchased

Molder
Variable
Successful?
Cost

Revenue

$208

$500

No

$252

$500

Yes

$104

$300

$126

$300