The cover girl company is expanding its operations and attempting to expand it sales territory. The sales manager has staff of experienced salespersons who are each paid $200 per week. He is planning to appoint some new sales trainers for $100 per week.
Based upon past experience, an experienced salesperson can generate $10,000 worth of sales per week. A sales trainee can generate an average of $6,000 worth of sales per week. The company has budgeted $800 for training new salespersons. The sales manager's payroll budget is $1,600 per week. Furthermore, the compnay has decided that sales force must be limited to 10 of fewer salespeople. The sales manager's decision problem is to find out the optimal number of experiences salespersons and new trainees in order to maximize total sales.
a. Formulate a linear programming model for this problem
b. Identify the optimal solution and its total sales using the graphical method
c. If the weekkls sales rate o fexperienced salespersons remains relatively constant at $10,000 per week, but weekly sales of trainees fluctutates widely, how much should the average sales per trainee per week be before the company should limit its sales staff to two experienced salespersons and eight trainees?
d. In the original problem, if the training cost per trainee is $200 rather than $100, how would the optimal solution change?
e. In the original problem, if the company increases the number of salespeople from 10 to 12, how would the optimal solution change?