Southstrom, a new department store in the Southeastern United States, needs to hire and train sales representatives to meet the growing customer demand and, in particular, to prepare for the

Christmas holiday shopping season. It is currently the end of June and Southstrom has 131 trained staff members. They need to develop a plan to hire and train additional sales representatives to meet the following minimum requirements for the coming months.

New sales representatives are trained by having them work with trained employees for one month. After that time they are considered fully trained and in subsequent months can work as trained staff members. Training the new staff members requires effort and energy on the part of the existing staff: each trainee requires $20 \%$ of the attention of a trained sales representative. For example, if we were to train 10 new staff members in any month, this would reduce the effective number of staff members available to work in sales in that month by 2 . Thus, as we develop a plan for staffing and training, we need to take into account the manpower required to do the training. A hiring, training and staffing schedule would complete a table like that of Table 1 below.

Southstrom's goal is to develop a training program that minimizes total costs, while meeting the minimum sales staff requirements given above. Trainees are paid $2,000 per month and trained sales representatives are paid $3,500 per month, regardless of whether they are working in sales or training; any "extra" staff capacity would work in sales and must be paid the full $3,500 per month. For now, you should assume that all trainees successfully complete the training program and that staff members cannot be fired, do not quit, and do not work overtime. All new hires start at the beginning of the month.

1. (10 points) Use the previous spreadsheet ("Southstrom") to formulate and solve an optimization model in Excel to find the optimal staffing plan. What is the total cost of the optimal plan?
2. (3 points) Rather than hiring and training new workers, suppose you could hire 10 additional experienced sales representatives temporarily who would work in November only at the regular monthly salary of $3,500. How would hiring these additional workers affect the total cost of staffing?
3. (3 points) Rather than hiring and training new workers, suppose you could hire 10 additional experienced sales representatives temporarily in December only at a premium monthly salary of $4,000. How would hiring these additional workers affect the total cost of staffing?
4. (3 points) Suppose that trainees had to be paid $3,500 per month like the fully trained staff members, rather than $2,000 per month. How would this affect the optimal staffing plan? How would it affect the total cost of staffing?
5. (6 points) Suppose that in addition to hiring and training workers, Southstrom could layoff some workers. These workers would be terminated at the beginning of the month (thus they would not available to work in the store that month) and would be paid $1,000 as a one-time severance payment. Reformulate the optimization problem to take into account the option to layoff workers. What is the new optimal stafing plan? What is the total cost of this optimal plan?
6. Extra Credit ( 5 points) Southstrom's personnel records indicate that $5 \%$ of the trained representatives leave the store at the end of each month. Moreover, 10\% of the trainees do not successfully complete the training program. These departing workers are not given any severance pay, but are paid for the full month of their departure. Using your model from Question 5 above, incorporate these attrition rates into your model. You should assume that the initial number of trained staff members at the end of June (131) is after June's departures and represents a starting point for July.

1. How does the attrition affect the optimal staffing plan?
2. How much should management be willing to pay for a plan that reduces the loss of trained staff from $5 \%$ to $4 \%$ per month?

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