A Children toy manufacturer conducts a job-training program for factory workers. Trained factory workers are used as certified trainers in the program at a ratio of one for every ten participants. The knowledge sharing program lasts for one month. From past experience it has been found that out of ten participants hired, only seven complete the program successfully (the unsuccessful employees are released). Trained factory workers are also needed for the next three are as follows: January 1000 February 1500 March 2000 In addition, the organization requires 2500 trained factory workers by April. There are 1300 trained factory workers available at the beginning of the year. Payroll costs per month are: Each Participant $400 Each trained Trainer 700 Each trained factory workers idle 500 Note: Union contract forbids firing trained factory workers

Set up the formulation of the model using three phase approach to the given problem that will produce the minimum cost hiring and training schedule and meet the organizations requirements.

Follow the three phase approach below to answer the question:

Phase 1. Identify the unknown variables to be determined (decision variables) and represent them in terms of algebraic symbols.

Phase 2. Identify all the restrictions or constraints in the problem and express them as linear equations or inequalities which are linear functions of the unknown variables.

Phase 3. Identify the objective or criterion and represent it as a linear function of the decision variables, which is to be maximized or minimized.