# A++ rating solution with detailed and correct expalination | Linear Programming Tutorial + Solution code for LINGO

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

The plant currently employs 350 fully trained technicians and project 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, recordkeeping, and 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 moth, 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 or in the research 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 or 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 \$2000 (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 Linear Programming.

(b)  Solve the problem. How many trainees must be given each month?

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