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Minneapolis Children's Hospital has been receiving numerous customer complaints because of its confusing, decentralized appointment and registration process. In an effort to reengineer its procedures and improve its customer service, the hospital has decided to centralize the process by establishing one call center devoted exclusively to appointments and registration. The call center will operate weekdays from 7 AM to 9 PM. A consulting firm has been contracted to analyze historical hospital data and forecast the number of calls the call center can expect to receive throughout the day. Table 1 summarizes the results of the firm's analysis. Table 1 Avg. Number of Calls Per Hour 40 85 Time Period 7 AM - 9 AM 9 AM - 11 AM 11 AM - 1 PM 1 PM - 3 PM 3 PM - 5 PM 5 PM - 7 PM 7 PM - 9 PM 70 95 80 35 10 Additionally, the consulting firm collected data on the mix of calls from Spanish speaking and English speaking customers. The hospital will have to hire both English speaking and Spanish speaking operators in order to be able to handle all calls (no bilingual operators are available). The data showed that, on average, 20 percent of the calls received were from Spanish speaking customers. Working with its human resources department, the call center project manager learns that telephone operators are able to handle an average of 6 calls per hours. The decision is made to set up two full-time shifts of 8 hours per day, one which starts at 7 AM and ends at 3 PM and one which starts at 11 AM and ends at 7 PM. Additionally, the call center will have the option of staffing on two part-time shifts of 4 hours per day, one which starts at 3 PM and ends at 7 PM and one which starts at 5 PM and ends at 9 PM. Full time operators will be paid $10.00 per hour and part-time operators will be paid $12.50 an hour. In addition to answering calls, full-time operators must spend two hours per day completing paperwork. While they are working on paperwork, operators are not available to handle incoming calls. Part-time operators are not assigned paperwork responsibilities. To balance the schedule, some of the full-time operators (on each of the two full-time shifts) can be tasked with doing their paperwork during the first two hours of their shift and some of the operators can do paperwork during the last two hours of their shift. The assignment of designated "paperwork time" is up to the call center manager. a. How many English-speaking operators and how many Spanish-speaking operators does the call center need during each two hour time period of the day in order to handle the forecasted call volume? b. Formulate a linear programming model to determine how to staff the call center in order to handle all calls while minimizing operating costs. Your answer should specify how many English speaking operators and how many Spanish speaking operators should be hired for each of the 4 available shifts (2 full-time and 2 part-time) and, for each of the two full-time shifts, how many of the operators should do their paperwork at the start of the shift and how many should do their paperwork at the end of the shift. C. After 6 months of successful call center operation, the call center manager decides to investigate training or hiring bilingual operators. If the call center revamps itself with all bilingual operators, what would the new staffing requirements be? What is the maximum percentage increase in the hourly wage rate that the call center manager can pay bilingual operators over monolingual operators without increasing total operating costs