Linear Programming

Phoenix Computer

1. The incremental salary and training cost associated with hiring a new employee and training him/her to be laptop specialist.

* Annual salary for new employee = $27,000 * Cost for three month training program = $1,500 per person * New employee undergoes three month training

$27,000/12 = $2,250
$2,250*3 months = $6,750 $6,750 + $1,500 =$8,250 per person
The incremental salary and training cost associated with hiring a new employee and training him/her to be laptop specialist is $8,250 per person.

2. The incremental salary and training cost associated with putting a current employee through the training program.

* Annual salary for new employee = $27,000 * Cost for two months training program = $1,000 * Current employee undergoes two months training.
$27,000/12 = $2,250 per month
$2,250*2 months = $4,500
$4,500 + $1,000 = $5,500 per person
The incremental salary and training cot associated with putting a current employee through the training program is $5,500 per person.

3. Recommendations regarding the hiring and training plan that will minimize the salary and training cost over February through August period.

New employee = N
Current Employee = C
Extra employee = E

Variables: Training Period

New employee undergoes three months training
N1 = February to April
N2 = March to May
N3 = April to June
N4 = May to July
N5 = Jun to August

Current employee undergoes two months training
C1 = March to April
C2 = April to May
C3 = May to June
C4 = June to July
C5 = July to August

Extra employee
E1 = Extra employee on May
E2 = Extra employee on June
E3 = Extra employee on July
E4 = Extra employee on August
E5 = Extra employee on September

Constraints:

Objectives = Minimize $8250(N1+N2+N3+N4+N5)+ $5500 (C1+C2+C3+C4+C5)+ $2250 (E1+E2+E3+E4+E5)

Subject to;
Laptop Specialist Needed
May: N1+C1-E1 = 20
June: