Refer to given Problem. Rockies Adventure Wear, Inc. has upgraded its order-processing centre in order to improve the processing speed and customer access rate. Before completely switching to the upgraded system, Rockies has an option of testing it. The test will cost Rockies S50 000, which includes the testing cost and loss of business due to shutting down the business for a half-day. If Rockies does not test the system, there is a 55% chance of severe failure ($150 000 repair and loss of business costs), a 35% chance of minor failure ($35 000 repair and loss of business costs), and a 10% chance of no failure.

If Rockies tests the system, the result can be favourable with the probability of 0.34, which requires no modification, and not favourable with the probability of 0.66. If the test result is not favourable, Rockies has two options: minor modification and major modification. The minor modification costs $5000 and the major modification costs $30 000. After the minor modification, there is still a 15% chance of severe failure ($150 000 costs), a 45% chance of minor failure ($35 000 costs), and a 40% chance of no failure. Finally, after the major modification, there is still a 5% chance of severe failure, a 30% chance of minor failure, and a 65% chance of no failure. Wha t is the recommended action for Rockies, using a decision tree analysis?

Problem :
Rockies Adventure Wear, Inc., sells athletic and outdoor clothing through catalogue sales. Its managers want to upgrade their order-processing centre so that thev have less chance of losing customers by putting them on hold. The upgrade may result in a processing capacity of 30, 40, 50, or 60 calls per hour with the probabilities of 0.2, 0.4, 0.3, and 0.1, respectively. Alarket research indicates that the average number of calls that Rockies may receive is 50 per hour.

(a) How many customers are expected to be lost per hour due to the lack of processing capacity?

(b) What is the variance of the loss due to the lack of processing capacity?