Question

The manager of a computer help center needs to determine a shift schedule for

his sta . The center is open from 8am until midnight (12am), and is divided into four shifts. The number of employees needed on each shift is as follows: 4 on the rst shift (8am-12pm), 10 on the second shift (12pm-4pm), 8 on the third shift (4pm-8pm), and 6 on the last shift (8pm-12am). Two types of employees can be hired to sta the computer center: full-time employees and part-time employees. Full-time employees must be hired for two consecutive shifts, and can be hired to start in the rst, second or third shift. Part-time employees are hired for a single shift. Full-time employees are paid $14 an hour, while part-time employees are paid $12 an hour. Lastly, during each of the shifts, there must be at least two full-time employees sta ed for every part-time employee.
Formulate a linear programming model to satisfy the stang requirements at minimum cost.

Answer 1

Step-by-step explanation:

we have to define certain variables in ordet for us to formulate the linear programming model

`aj =` the number of full time staff hired at time j

`bj=` number of full time staff hired at time j

1 full time emploer 8hrs x 14$

= 112 dollars

1 part time worker = 4hrs x $12

= 48 dollars

we set up the model as:

`minimize 112(a_(1) +a_(2) +a_(3) )+48(b_(1) +b_(2) +b_(3))`

`a_(1) + b_(1) = 4`

`a_(1) +a_(2) +b_(2) = 10`

`a_(2) +a_(3) +b_(3) =8`

`a_(3) +b_(4) =6`

`a_(1) >2b_(1)`

`a_(1) +a_(2) \geq 2b_(2)`

`a_(2) +a_(3) \geq 2b_(3)`

`a_(3) \geq 2b_(4)`

`a_(j) ,b_(j) \geq 0`

∀j