Just need help with part E

A small call center, staffed by only one operator (server), has 20 customers calling every hour with a standard deviation of inter-arrival times of 3 minutes. (This results in a 2 = 1.) The activity time for a call center operator to process each call (by addressing the caller's queries) is, on average, 2.5 minutes with a standard deviation of 8 minutes (or a 2 = 10.24), primarily because of the wide variety of caller queries. (Hint: Consider these processing times to be General not Exponential.) ROUND ALL ANSWERS TO 2 DECIMAL PLACES a. In minutes, what is the average time that a caller has to wait in line before getting served by the call center operator? 70.25 b. What is the average number of callers who are in the call center system (either waiting or being served by the operator)? 24.25 c. What is the probability that the server will be busy? 0.83 Suppose that for every minute of time a caller waits for service the call center is required to pay out a penalty of 60 cents. The cost of hiring a qualified call center operator (identical to the current operator) is $15 per hour. d. What is the estimated hourly penalty pay out by the call center for caller wait time? (Hint: To answer this question, consider how long the average customer spends waiting in line and how many customers arrive in an hour.) 14.05 e. The call center is trying to decide how many new operators to hire. Compute the estimated hourly costs for the given number of new operators. Hourly Penalty Hourly Operator Scenario Hourly Total Cost Cost Cost Hire 1 more operator for a total of 2 Hire 2 more operators for a total of 3 Hire 3 more operators for a total of 4 Hire 4 more operators for a total of 5 A small call center, staffed by only one operator (server), has 20 customers calling every hour with a standard deviation of inter-arrival times of 3 minutes. (This results in a 2 = 1.) The activity time for a call center operator to process each call (by addressing the caller's queries) is, on average, 2.5 minutes with a standard deviation of 8 minutes (or a 2 = 10.24), primarily because of the wide variety of caller queries. (Hint: Consider these processing times to be General not Exponential.) ROUND ALL ANSWERS TO 2 DECIMAL PLACES a. In minutes, what is the average time that a caller has to wait in line before getting served by the call center operator? 70.25 b. What is the average number of callers who are in the call center system (either waiting or being served by the operator)? 24.25 c. What is the probability that the server will be busy? 0.83 Suppose that for every minute of time a caller waits for service the call center is required to pay out a penalty of 60 cents. The cost of hiring a qualified call center operator (identical to the current operator) is $15 per hour. d. What is the estimated hourly penalty pay out by the call center for caller wait time? (Hint: To answer this question, consider how long the average customer spends waiting in line and how many customers arrive in an hour.) 14.05 e. The call center is trying to decide how many new operators to hire. Compute the estimated hourly costs for the given number of new operators. Hourly Penalty Hourly Operator Scenario Hourly Total Cost Cost Cost Hire 1 more operator for a total of 2 Hire 2 more operators for a total of 3 Hire 3 more operators for a total of 4 Hire 4 more operators for a total of 5