During lunch time, customers arrive at a postal office at a rate of lambda equals 36 per hour. The interarrival time of the arrival process can be approximated with an exponential distribution. Customers can be served by the postal office at a rate of mu equals 45 per hour. The service time for the customers can also be approximated with an exponential distribution. For each of the following questions, show your work and use the right notation. Required:
a. Determine the utilization factor.
b. Determine the probability that the system is idle, i. e., no customer is waiting or being served.
c. Determine the probability that exactly one customer is in the system, i. e., no customer is waiting but one is served.

Vulcan company is a monthly depositor whose tax liability for march 2019 is $2,510. 1. what is the due date for the deposit of these taxes? march 17 2. assume that no deposit was made until april 29. compute the following penalties. assume a 365-day year in your computations. round your answers to the nearest cent. a. penalty for failure to make timely deposits. $ b. penalty for failure to fully pay employment taxes $ c. interest on late payment (assume a 5% interest rate). $ d. total penalty imposed $

Symantec corp., located in cupertino, california, is one of the world's largest producers of security and systems management software. the company's consolidated balance sheets for the 2009 and 2008 fiscal years included the following ($ in thousands): current assets: receivables, less allowances of $21,766 in 2009 and $24,089 in 2008 $ 838,010 $ 758,700 a disclosure note accompanying the financial statements reported the following ($ in thousands): year ended 2009 2008 (in thousands) trade accounts receivable, net: receivables $ 859,776 $ 782,789 less: allowance for doubtful accounts (8,938) (8,990) less: reserve for product returns (12,828) (15,099) trade accounts receivable, net: $ 838,010 $ 758,700 assume that the company reported bad debt expense in 2009 of $2,000 and had products returned for credit totaling $3,230 (sales price). net sales for 2009 were $6,174,800 (all numbers in thousands).required: what is the amount of accounts receivable due from customers at the end of 2009 and 2008? what amount of accounts receivable did symentec write off during 2009? what is the amount of symentec’s gross sales for the 2009 fiscal year? assuming that all sales are made on a credit basis, what is the amount of cash symentec collected from customers during the 2009 fiscal year?

Needs to schedule the staffing of the center. it is open from 8am until midnight. larry has monitored the usage of the center at various times of the day and determined that the following number of computer consultants are required: time of dayminimum number of consultants required to be on duty8 am-noon4noon-4 pm84pm-8pm108pm-midnight6 two types of computer consultants can be hired: full-time and part-time. the full- time consultants work for eight consecutive hours in any of the shifts: morning (8am- 4pm), afternoon (noon-8pm) and evening (4pm-midnight). full-time consultants are paid $14 per hour. part-time consultants can be hired to work any of the four shifts listed in the table. part-time consultants are paid $12 per hour. an additional requirement is that during every time period, there must be at least two full-time consultants on duty for every part-time consultant on duty. larry would like to determine how many full-time and part-time consultants should work each shift to meet the above requirements at the minimum possible cost. formulate this as an lp problem. you must define your variables clearly