Lenny also knows that he has both fulltime and parttime workers available to staff the call center. A full-time employee works 8 hours per day, but because of paperwork that must also be completed, the employee spends only 4 hours per day on the phone. To balance the schedule, the employee alternates the 2hour shifts between answering phones and completing paperwork. Fulltime employees can start their day either by answering phones or by completing paperwork on the first shi.ft . The full -ti:|:ne employees speak either Spanish or English , but none of them are bilingual .Both Spanish-speaking and Englishspeaking employees are paid 510 per hour for work before 5 P.M. and 512 per hour for work after 5 RM. The full-time employees can begin work at the beginning of the I" A.M. to 9 A.M. shift, 9 A.M. to 11 ELM. shift, 11 A.M. to 1 PM. shift, or 1 P.MI. to 3 PJVI. shift. The part-time employees work for r; hours, only answer calls, and only speak English. They can start work at the begirmmg of the 3 P.M.to 5 P.M. shift or the 5 P.M. to 3' PM. shift, and like the full-time employees, they are paid $10 per hour for work before 5 P.M. and 512 per hour for work after 5 PJVI. For the following analysis consider only the labor cost for the time employees spend answering phones. The cost .for paperwork time is charged to other cost centers. {a} How many Spanish-speaking operators and how many Englishspeaking operators does the hospital need to staff the call center during each 2hour shift of the day in order to answer all calls ? Please provide an integer number since half a human operator makes no sense. (b) Lerlny needs to determine how many fulltime employees who speak Spanish , fulltime employees who speak English, and part-time employees he should hire to begin on each shift. Creative Chaos Consultants advise him that linear programming can be used to do this in such a way as to minimize operating costs while answering all calls. Formulate a linear programming (LP) mode} of this problem. {c} Obtain an optimal solution for the model formulated in part (b) to guide Lenny's decision. {d) Because many fulltime workers do not w ant to work late into the evening, Lenny can find only one qualified English-speaking operator willing to begin work at l P.M. Given this new constraint, how many fulltime Englishspeaking operators, full-time Spanishspeaking operators, and part time operators should Lenny h.1'.re for each shift to minimize operating costs while answering all calls? {e} Lenny now has decided to investigate the option of hiring bilingual operators instead of monolingual operators. If all the operators are bilingual, how many operators should be working during each 2hour shift to answer all phone calls? As in part (a), please provide an integer answer. {f }| If all employees are bilingual, how many fulltime and parttime employees should Lenny hire to begin on each shift to minimize costs? As in part (b), formulate a LP model to guide Lenny's decision. {gj \"that is the maximum percentage increase in the hourly wage rate that Lenny can pay bilingual employees over monolingual employees without increasing the total operating costs? {h} 'Nhat other features should Lenny explore to improve service or minimize operating costs
