An electricity company operates a call center and serves its customers 24 hours a day. On...

 

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An electricity company operates a call center and serves its customers 24 hours a day. On average customers wait for 5 minutes before their calls are answered under the existing system. The company has a policy that if customers wait for longer than 15 minutes, they are entitled to claim $100 off their next quarterly bill. That is a penalty cost for the company's low responsiveness. The company's director wants to hire more customer services officers to serve more customers and gain cost saving through a new system. If the company will hire more customer services officers, at an extra daily expense of $500, the customer's average waiting time can be reduced to 4 minutes. The new system is only worthwhile if the probability that a customer waits for longer than 15 minutes is reduced by at least 0.025, and the penalty cost reduction is higher than the extra daily expense. Assume that the waiting times in the existing and new systems follow the Exponential distribution. Round your answers to 4 decimal places. Q1A) Determine the probability that a customer waits for more than 15 minutes under the existing system. Q1B) Determine the probability that a customer waits for more than 15 minutes under the new system (i.e., with more customer services officers). Q1C) Determine the change of probability based on your answers in Q1A and Q1B. Q1D) Determine the average number of answered calls per day under the new system. Q1E) Determine the average daily penalty cost under the existing system. Q1F) Determine the average daily penalty cost under the new system. Q1G) Should more customer services officers be hired? An electricity company operates a call center and serves its customers 24 hours a day. On average customers wait for 5 minutes before their calls are answered under the existing system. The company has a policy that if customers wait for longer than 15 minutes, they are entitled to claim $100 off their next quarterly bill. That is a penalty cost for the company's low responsiveness. The company's director wants to hire more customer services officers to serve more customers and gain cost saving through a new system. If the company will hire more customer services officers, at an extra daily expense of $500, the customer's average waiting time can be reduced to 4 minutes. The new system is only worthwhile if the probability that a customer waits for longer than 15 minutes is reduced by at least 0.025, and the penalty cost reduction is higher than the extra daily expense. Assume that the waiting times in the existing and new systems follow the Exponential distribution. Round your answers to 4 decimal places. Q1A) Determine the probability that a customer waits for more than 15 minutes under the existing system. Q1B) Determine the probability that a customer waits for more than 15 minutes under the new system (i.e., with more customer services officers). Q1C) Determine the change of probability based on your answers in Q1A and Q1B. Q1D) Determine the average number of answered calls per day under the new system. Q1E) Determine the average daily penalty cost under the existing system. Q1F) Determine the average daily penalty cost under the new system. Q1G) Should more customer services officers be hired?