Linear Programming Staffing Problem

(Nuclear plant staffing problem) South Central Utilities has just announced the August 1 opening its second nuclear generator at its Baton Rou, Louisiana, nuclear power plant. Its personnel department has been directed to determine how many nuclear technicians need to be hired and trained the remainder of the year.

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

MONTH PERSONNEL HOURS NEEDED
August 40,000
September 45,000
October 35,000
November 50,000
December 45,000

By Louisiana law, a reactor employee can actually work no more than 130 hours per month. (Slightly over one hour per day is used for check-in and checkout, recordkeeping, and for daily radiation health scans.) Policy at South Central Utilities also dictates that layoffs are not acceptable in those months when the nuclear plant is overstaffed. So, if more trained employees are available than are needed in any month, each worker is still fully paid, even though It or she is not required to work the 130 hours.

Training new employees is an importantly costly procedure. It takes one month of one-to-one classroom instruction before a new technician is permitted to work alone in the reactor facility. Therefore South Central must hire trainees one month before they are actually needed. Each trainee teams up with a skilled nuclear technician and requires 90 hours of that employee's time, meaning that 90 hours less of the technician's time are available that month for actual reactor work.
Personnel department records indicate a turnover rate of trained technicians at 5% per month. In other words, about 5% of the skilled employees at the start of any month resign by the end of that month. A trained technician earns an average monthly salary of $2,000 (regardless of the number of hours worked, as noted earlier). Trainees are paid $900 during their one month of instruction.

(a) Formulate this staffing problem using LP.
(b) Solve the problem. How many trainees must begin each month?