Far North Outfitters is a retail phone-catalogue company that specializes in outdoor clothing and equipment. A phone station at the company will be staffed with either full-time operators or temporary operators 8 hours per day. Full-time operators, because of their experience and training, process more orders and make fewer mistakes than temporary operators. However, temporary operators are cheaper because of a lower wage rate, and they are not paid benefits. A full-time operator can process about 360 orders per week, whereas a temporary operator can process about 270 orders per week. A full-time operator will average 1.1 defective orders per week, and a part-time operator will incur about 2.7 defective orders per week. The company wants to limit defective orders to 200 per week. The cost of staffing a station with full-time operators is $610 per week, and the cost of a station with part-time operators is $450 per week. Using historical data and forecasting techniques, the company has developed estimates of phone orders for an eight-week period as follows: Weeks Orders 1 19,500 2 21,000 3 25,600 4 27,200 5 33,400 6 29,800 7 27,000 8 31,000 The company does not want to hire or dismiss full-time employees after the first week (i.e., the company wants a constant group of full-time operators over the eight-week period). The company wants to determine how many full-time operators it needs and how many temporary operators to hire each week in order to meet weekly demand while minimizing labor costs.
a) Formulate and solve a linear programming model for this problem.