Example 1

Arthrodax Company has been approached by Ranger Sound with a rush order offer to purchase 100 units
of a customized version of Arthrodax's SoundScreamer audio mixer at $5,000 per unit, and Arthrodax
needs to decide how to respond. The electronic modifications of the standard SoundScreamer needed
for this customized version are straightforward, but there will be a fixed cost of $100,000 to
design the modifications and set up for assembly of the customized Sound-Screamers, regardless of
the number of units produced. It will cost $2,000 per unit to manufacture the circuit boards for
the units. Since Arthrodax has some short term spare manufacturing capacity, the Ranger offer is
potentially attractive. However, the circuit boards for the customized units will not Ż t into the
standard SoundScreamer case, and Arthrodax must decide what to do about acquiring cases for the
customized units as it decides whether to accept Ranger's purchase offer. An appropriate case can
be purchased at $500 per case, but Arthrodax could instead purchase an injection molder to make the
cases. It will cost $20,000 to purchase the molder, and there is a 0.6 probability that it will be
possible to successfully make the cases using the molder. If the molder does not work, then the
purchase price for the molder will be totally lost and Arthrodax must still purchase the cases at
$500 per case. If the molder works, then it will cost $60 per case to make the cases using the
molder. Regardless of which case is used, the cost of assembling the SoundScreamer circuit boards
into the case is $20  per unit. Unfortunately, there is no way to test the molder without
purchasing it. Assume that there is no other use for the molder except to make the cases for the
Ranger order.

(i)                              Draw a decision tree for Arthrodax's decision about whether to
accept the  Ranger o® er and how to acquire the cases for the customized SoundScreamers.

(ii)                             Using expected net profit as the decision criterion, determine the
preferred course of action for Arthrodax


Example 2

This is a continuation of Example 1.. Assume that all information given in that exercise is still
valid, except as discussed in this exercise. Ranger now tells Arthrodax that there is uncertainty
about the number of customized SoundScreamers that will be needed. Specifically, there is a 0.35
probability that it will need 100 units, and a 0.65 probability that it will need 50 units. If
Arthrodax will agree now to produce either number of units, then Ranger will pay $6,000 per unit if
it ultimately orders 50 units, and will pay $5,000 per unit if it ultimately orders 100 units. The
timing is such on this rush order that Arthrodax will have to make a decision about purchasing the
injection molder before it knows how many units Ranger will take. However, Arthrodax will only need
to purchase or manufacture the number of circuit boards and cases needed for the Ż nal order of
either 50 or 100 units.

(i)                  Draw a decision tree for Arthrodax's decision about whether to accept the
Ranger o® er and how to acquire the cases for the customized SoundScreamers. Note that this is a
situation with dependent uncertainties, as discussed in Section 1.3.

(ii)            Using expected net profit as the decision criterion, determine the preferred course
of action for Arthrodax.