The Phone Shopping Center sells products by displaying products on television and taking orders by telephone. The hours of operation are 8:00 A.M. to 5:00 P.M. The minimum number of operators needed at different times of the day has been determined, as shown in the table below. Time Minimum number of operators needed 8:00 A.M. - 9:00 A.M. 15 9:00 A.M. - 10:00 A.M. 10 10:00 A.M. - 11:00 A.M. 18 11:00 A.M. - 12:00 Noon 14 12:00 Noon - 1:00 P.M. 15 1:00 P.M. - 2:00 P.M. 16 2:00 P.M. - 3:00 P.M. 20 3:00 P.M. - 4:00 P.M. 18 4:00 P.M. - 5:00 P.M. 16 The center may be staffed by full-time employees who start at 8:00 A.M. and leave at 4:00 P.M., and by part-time employees who work five consecutive hours. The cost for a full-time employee is $45 per day (including salary and benefits), while a part-time employee costs $30 for five hours. The number of full-time employees cannot exceed 15. The company wishes to minimize cost. Formulate this as a linear programming problem and answer the following questions: a) How may full-time employees should be used? b) How many part-time employees should be reporting for work at each of the different hours during the day? c) What is the minimum total cost? d) How many employees start to work at 11:00am? e) How many employees work during 11am and 12 noon?