3) South Central Utilities has just announced that it will open a new nuclear power generator at its Baton Rouge, Louisiana nuclear power plant. Its personnel depart has been directed to determine how many technicians need to be hired and trained over the remainder of the year.

The plant currently employs 350 fully trained technicians and projects the following personnel needs

Month	August	September	October	November	December
Hours Needed	40,000	45,000	35,000	50,000	45,000

By Louisiana law, a reactor technician can work no more than 130 hours a month (slightly more than 1 hour per day is needed to sign in and out, review records, and undergo a health check for exposure). Policy at South Central Utilities also dictates that layoff of trained technicians is not allowed during periods of slack time. So if more technicians are available than needed in any month each worker is still paid even though they may not work the full 130 hours.

Training new workers is an important and costly procedure. It takes one month of one on one classroom instruction before a technician can be certified to operate in a nuclear facility. Therefore, South Central must hire trainees one month before they are needed in the facility. Each trainee is matched up with a trained technician and requires 90 hours of the technicians time, meaning that the trained technicians have 90 fewer hours to work in the facility that month if they are training.

Personnel department records indicate that the turnover rate of trained technicians is 5% a month due to technicians quitting, being fired, losing certification, or for health reasons. This means that in any month the number of trained technicians is the new trained technicians and only 95% of the total trained technicians of the previous month. A trained technician gets paid an average of $2,000 a month while trainees are paid an average of $900 a month while they are training.

X is the number of fully trained technicians for that month and T is the number of trainees for that month. Months are numbered August = 1, September = 2 December = 5.

a) How many trainees must be hired each month?

b) What is the expected cost for technicians and trainees over the last five months of the year?