Road Rambler sells specialty running shoes and apparel through catalogs and the Web. Customers can phone in orders at any time day or night, seven days a week. During the 4 a.m. to 8 a.m. shift, a single sales rep handles all calls. During this time, calls arrive at a rate of 18 per hour following a Poisson distribution. It takes the sales rep an average of 3 minutes to process each call. The variability in service times is approximately exponentially distributed. All calls received while the sales rep is busy are placed in a queue. (a) On average, how long (in minutes) must callers wait before talking to the sales rep? (Round your answer to the nearest integer.) __ minutes (b) On average, how many customers are on hold? (Round your answer to four decimal places.) customers (c) What is the probability that the customer will be placed on hold? (Round your answer to four decimal places.) (d) What is the sales rep's utilization rate (in percent)? (Round your answer to two decimal places.) _ % (e) Suppose Road Rambler wants there to be no more than a 10% chance that a customer will be placed on hold. How many sales reps should the company employ? They should employ at least __ sales reps.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Road Rambler sells specialty running shoes and apparel through catalogs and the Web. Customers can phone in orders at any time day or night, seven days a week. During the 4 a.m. to 8 a.m. shift, a single sales rep handles all calls. During this time, calls arrive at a rate of 18 per hour following a Poisson distribution. It takes the sales rep an average of 3 minutes to process each call. The variability in service times is approximately exponentially distributed. All calls received while the sales rep is busy are placed in a queue.

(a) On average, how long (in minutes) must callers wait before talking to the sales rep? (Round your answer to the nearest integer.)

______ minutes

(b) On average, how many customers are on hold? (Round your answer to four decimal places.)

______ customers

(d) What is the sales rep's utilization rate (in percent)? (Round your answer to two decimal places.)

_______ %

(e) Suppose Road Rambler wants there to be no more than a 10% chance that a customer will be placed on hold. How many sales reps should the company employ?

They should employ at least ______ sales reps.

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