Question

MOVIES Employees at a local movie theater work overlapping 8-hour shifts from noon to 8 P.M. or from 4 P.M. to midnight. The table below shows the number of employees needed and their corresponding pay. Find the numbers of day-shift workers and night shift workers that should be scheduled to minimize the cost. What is the minimal cost?​

Answer 1

Answer:

8 day shift and 6 night shift. minimal cost is $776

Step-by-step explanation:

Answer 2

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

$\begin{array}{|l|c|c|c|} \mathbf{Time}& \mathbf{12 \ noon \ -\ 4 \ p.m.}& \mathbf{4 \ p.m. \ -\ 8 \ p.m. }& \mathbf{ 8 \ p.m. \ - midnight}\\Employee \ needed&At \ least \ 5&At \ least \ 14 &6\\Hourly \ rate& \ 5.50 & \ 7.50 & \ 7.50 \end{array}\right]$

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:

brainly.com/question/13610156

brainly.com/question/20022290