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:

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 fulltime 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.
b. Far North Outfitters is going to alter its staffing policy. Instead of hiring a constant group of full-time operators for the entire eight-week planning period, it has decided to hire and add full-time operators as the eight-week period progresses, although once it hires full-time operators it will not dismiss them. Reformulate the linear programming model to reflect this altered policy and solve to determine the costsavings

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Weeks Orders 19,500 21,000 25,600 27,200 Weeks Orders 33,400 29,800 27,000 31,000