The bank is working to develop an efficient work schedule for full-time and part-time tellers. the schedule must provide for efficient operation of the bank, including adequate customer service, employee breaks, and so on. on fridays, the bank is open from 9: 00 a. m. to 7: 00 p. m. the number of tellers necessary to provide adequate customer service during each hour of operation is summarized here. time no. of tellers time no. of tellers 9: 00 a. m.-10: 00 a. m. 6 2: 00 p. m.-3: 00 p. m. 6 10: 00 a. m.-11: 00 a. m. 4 3: 00 p. m.-4: 00 p. m. 4 11: 00 a. m.-noon 8 4: 00 p. m.-5: 00 p. m. 7 noon-1: 00 p. m. 10 5: 00 p. m.-6: 00 p. m. 6 1: 00 p. m.-2: 00 p. m. 9 6: 00 p. m.-7: 00 p. m. 6 each full-time employee starts on the hour and works a 4-hour shift, followed by a 1-hour break and then a 3-hour shift. part-time employees work one 4-hour shift beginning on the hour. considering salary and fringe benefits, full-time employees cost the bank $15 per hour ($105 a day), and part-time employees cost the bank $8 per hour ($32 per day).

(b) solve the lp relaxation of your model in part (a). if required, round your answers to the nearest whole number.

(c) solve for the optimal schedule of tellers.

(d) after reviewing the solution to part(c), the bank manager realized that some additional requirements must be specified. specifically, she wants to ensure that one full-time employee is on duty at all times and that there is a staff of at least five full-time employees. revise your model to incorporate these additional requirements, and solve for the optimal solution. if required, round your answers to the nearest whole number.