PLEASE READ NOTE BELOW QUESTION BEFORE POSTING SOLUTION. An electronics company runs a web-based sales business model. To support customers trying to order products, the company has one person in their sales department that operates three telephone lines. They have a single person taking calls and the other two lines are used to put people on hold. If the sales rep is helping a customer and the other two lines have callers on hold, additional callers cannot get through. It is observed that most people who are unable to get through end up not ordering anything from the website. The average completed sale results in $80 profit for the company. Over the last 6 months, the business receives averages 6 calls per hour. The sales representative only requires an average of 3 minutes to service the call and complete the sale. Assume nobody on hold hangs up. Note: This question has been posted before and the solution given is INCORRECT! Please understand that the following assumptions are INVALID: If 1 call is covered in 3 minutes, then in 1 hour, or 60 minutes, 20 calls could have been completed but only 6 calls are done, so lost calls per hour are 14. The problem states that the company receives 6 calls per hour, therefore, the assumption of 14 missed calls per hour is wrong. This must be solved using queuing theory.
a) What is the expected number of lost calls per hour? Estimate how much profit the company is losing as a result.
b) Three options are posed to address this issue. Determine the benefit of each and make a recommendation on which option to select or do nothing. Option 1. Hire an additional sales representative to service calls. The existing sales rep charges $10/hour. Option 2. Purchase an additional phone line for $300/month Option 3. Hire an IT firm to fix the website. The changes are estimated to reduce the number of service calls from 6 per hour to 4 per hour. An IT firm provided a quote to accomplish this for $8,000.00