Linear Programming

How important is it that I actually finish this problem? It is only 1 question of my homework assignment.

Problem 3.42

South Central Utilities has just announced the August 1 opening of its second nuclear generator at its Baton Rouge, LA nuclear power plant. Its personnel department has been directed to determine how many nuclear 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 - 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 1 hour per day is used for check-in and check-out, record keeping, and daily radiation health scans.) Policy at South Central Utilities also dictates that layoffs are not acceptable in those months when the nuclear plan is overstaffed. So, if more trained employees are available than are needed in any month, each worker is still fully paid, even though he or she is not required to work the 130 hours.

Training new employees is an important and costly procedure. It takes one month of one-on-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 the employee's time, meaning that 90 hours less of the technician's time are available that month for actual work.

Personnel department records indicate a turnover rate of trained technicians at 2% per month. In other words, 2% of the skilled technicians at the start of any month resign by the end of that month. A trained technician earns a monthly salary of $4,500 while trainees are paid $2,000 during their one month instruction.

Formulate this staffing problem using LP and solve it by using Excel.