In linear programming the constraints and the objective function are composed of linear decision variables
The schedule that minimize the cost is to have;
8 day-shift workers and 6 night shift workers
The given parameter are;
The overlapping shift worked are;
Noon to 8 P.M.
4. P.M. to midnight
[tex]\begin{array}{|l|c|c|c|} \mathbf{Time}& \mathbf{12 \ noon \ -\ 4 \ p.m.}& \mathbf{4 \ p.m. \ -\ 8 \ p.m. }& \mathbf{ 8 \ p.m. \ - midnight}\\Employee \ needed&At \ least \ 5&At \ least \ 14 &6\\Hourly \ rate& \$5.50 & \$7.50 & \$7.50 \end{array}\right][/tex]
Let x represent the number of day-shift workers required, and let y represent the number of night shift workers required, we have;
x + y ≥ 14
y = 6
x ≥ 5
By plugging in the value of y, gives;
x + 6 ≥ 14
x ≥ 14 - 6 = 8
x ≥ 8
Therefore, the solution for minimal cost that satisfies the constraints is x = 8
We get;
The schedule to minimize the cost is; The number of day-shift workers required, x = 8, and the number of night shift workers required, y = 6
Learn more about optimization and linear programming here:
https://brainly.com/question/13610156
https://brainly.com/question/20022290
