P14.8 Decision Trees. Keystone Manufacturing, Inc., is analyzing a new bid to supply the compa- ny with electronic control systems. Alpha Corporation has been supplying the systems, and Keystone is satisfied with its performance. However, a bid has just been received from Beta Controls, Ltd., a firm that is aggressively marketing its products. Beta has offered to supply systems for a price of $120,000. The price for the Alpha system is $160,000. In addition to an attractive price, Beta offers a money-back guarantee. That is, if Beta’s systems do not match Alpha’s quality, Keystone can reject and return them for a full refund. However, if it must reject the machines and return them to Beta, Keystone will suffer a delay costing the firm $60,000.
A. Construct a decision tree for this problem and determine the maximum probability that Keystone could assign to rejection of the Beta system before it would reject that firm’s offer, assuming that it decides on the basis of minimizing expected costs.
B. Assume that Keystone assigns a 50% probability of rejection to the Beta Controls. Would Keystone be willing to pay $15,000 for an assurance bond that would pay $60,000 in the event that the Beta Controls fail the quality check? (Use the same objective as in part A.) Explain.