Please check the complete question and then answer it.

A machine tool company conducts a job training program for machinists. Trained machinists are used as trainers in the program at the ratio of 1 for every 10 trainees. The training program lasts for one month. From past experience it has been found that out of 10 trainees hired, only 7 complete the program successfully, the unsuccessful trainees are quitted from the company.

Trained machinists are also needed for machining and the companys requirements for the next 3 months, January to March, are 100, 150, and 200 respectively. In addition, the company requires 250 trained machinists by April. There are 130 trained machinists available at the beginning of January. Payroll costs per month for trainee and trained machinist are $1,000 and $1,800, respectively.

Find the optimal solution to above LP problem by the simplex method.