A software company conducts a job-training program for managers in its marketing department. Trained managers are used as teachers in the program at a ratio of one for every ten trainees. The training program lasts for one month. From past experience it has been found that out of ten trainees hired, only seven complete the program successfully (the unsuccessful trainees are released).

Trained managers are also needed for management, and the company's requirements for trained managers to perform management for the next three months are as follows:

January 100

February 150

March 200

In addition, the company requires 250 trained managers by the beginning of April. There are 130 trained managers available at the beginning of the year. Payroll costs per month are:

Each trainee $4000

Each trained manager $7000 (Managing or teaching)

Each trained manager idle $5000 (Union contract forbids firing a trained manager)

The company plans to hire managers and trainees at the beginning of January, February, and March, but not April. Fractional hires are possible due to part-time arrangements. Find a schedule for hiring managers and trainees that will meet the company's requirements while minimizing their staffing costs.