Arthrodax Company has accepted a rush order from Ranger Sound for 100 units of a customized version of Arthrodax's SoundScreamer audio mixer. The customized units will not fit the standard SoundScreamer case. Arthrodax could purchase cases from another company in which case their profit from the rush order would be $260,000.

Alternatively, Arthrodax can purchase an injection molder and try to make the cases them- selves. There is some uncertainty about whether it will be possible to successfully make the cases using the molder. Unfortunately, there is no way to test the molder without purchasing it. Arthrodax estimates that there is a 0.65 probability that they can successfully make the cases with the molder, in which case their profit from the rush order would be $280,000. If the molder does not work, then the purchase price for the molder will be totally lost and Arthrodax must still purchase the cases. In this case their profit from the rush order would be $240,000.

(a) Use Bayes' rule to determine whether or not Arthrodax should purchase the molder. (b) What is the expected value of perfect information for this decision?

(c) If Arthrodax has a utility of 0.6 for $260,000 are they risk seeking, risk neutral, or risk averse?

(d) Suppose that Ranger Sound changes their order to 55 units, which reduces profits from the three scenarios described above from $260,000, $280,000, and $240,000 to $153,000, $155,000, and $133,000, respectively. Use Bayes' rule to determine whether or not Arthrodax should purchase the molder.

(e) Suppose that Ranger Sounds tells Arthodax that there is uncertainty about the number of units it will need. Specifically, there is a 0.25 probability that it will order 100 units and a 0.75 probability that it will only order 55 units. The timing is such that Arthodax will need to make a decision about purchasing the injection molder before knowing how many units Ranger Sound will order. (i) Use Bayes' rule to determine whether or not Arthrodax should purchase the molder. (ii) What is the expected value of perfect information for this decision?