. (10 points) Century Cast is a Cable/Internet service company and provides online live-chat customer support. Chats are categorized into three types: account support, billing support, and technical support. Each type of call arrives according to a Poisson distribution with a mean rate of 12, 20, and 10 per hour respectively for account support, billing support, and technical support. Please use the appropriate queueing Excel template to answer these questions. a. (5 points) Century Cast is considering cross-training the chat representatives to be capable of handling all three types of chats. The time it takes for a representative to handle any one of the chat types follows an exponential distribution with a mean of 10 minutes. Assume each chat representative chats with one customer at a time. The goal for Century Cast is that 90% of the time a chat representative responds to a customer within 1 minute of the initial request. How many chat representatives should be hired and trained to achieve this goal? Please indicate how you used the Excel templates to arrive at this decision. (5 points) Century Cast could choose to hire and train two groups of chat representatives. The first group is capable of responding to all account support and billing support chats, and the representatives can handle these two types of chats following an exponential distribution with a mean time of 8 minutes. The second group of representatives focuses on technical support chats and their chats will follow an exponential distribution with a mean of 9 minutes. For this alternative, Century Cast will have 8 representatives in the first group and 3 representatives in the second group. Will this achieve the goal (90% of the time a chat representative responds to a customer within 1 minute of the initial request)? Please indicate how you used the template to arrive at this decision