2. (50pts) A furnace repair company estimates that number of hours of skilled repair time that it requires during the next four months is as follows: At the beginning of the first month, 50 skilled repair technicians work for the company. Each skilled repair technician can work up to 160 hours a month. To meet future demands, new repair technicians must be trained. It takes one month to train a new technician. During the month of training, a trainee must be supervised for 50 hours by an experienced technician; experienced technicians cannot perform other work when supervising trainees. Each experienced repair technician is paid $3,000 a month (even if he or she does not work the full 160 hours). During the month of training, a trainee is paid $1,500 a month. a) Formulate a Linear Programming Model that will enable the company to minimize the labor cost incurred in meeting the labor requirements for the next four months. Clearly define 1) the decision variables, 2) the objective function, 3) the constraints. b) Suppose now that at the end of each month, 3\% of the company's experienced repair technicians quit their job. In addition, 5% of the trainees leave after their initial month of training. Show how you can incorporate these factors into your LP formulation. 2. (50pts) A furnace repair company estimates that number of hours of skilled repair time that it requires during the next four months is as follows: At the beginning of the first month, 50 skilled repair technicians work for the company. Each skilled repair technician can work up to 160 hours a month. To meet future demands, new repair technicians must be trained. It takes one month to train a new technician. During the month of training, a trainee must be supervised for 50 hours by an experienced technician; experienced technicians cannot perform other work when supervising trainees. Each experienced repair technician is paid $3,000 a month (even if he or she does not work the full 160 hours). During the month of training, a trainee is paid $1,500 a month. a) Formulate a Linear Programming Model that will enable the company to minimize the labor cost incurred in meeting the labor requirements for the next four months. Clearly define 1) the decision variables, 2) the objective function, 3) the constraints. b) Suppose now that at the end of each month, 3\% of the company's experienced repair technicians quit their job. In addition, 5% of the trainees leave after their initial month of training. Show how you can incorporate these factors into your LP formulation