Introduction to Management Science 12th Edition by Bernard Taylor

Exercise 73

Great Northwoods Outfitters is a retail phone-catalog 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 they receive a lower wage rate and 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 averages 1.1 defective orders per week, and a part-time operator incurs 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 8-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 8-week period). The company wants to determine how many full-time operators it needs and how many temporary operators to hire each week to meet weekly demand while minimizing labor costs.
a. Formulate a linear programming model for this problem.
b. Solve this model by using the computer.