10- Suppose that the minimum number of security staff required at different hours are at the ith hour (i=1,2,…,24) are outlined as follows:
|
Hour beginning at |
12am |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
|
Number of staff required |
5 |
4 |
4 |
4 |
4 |
6 |
6 |
6 |
8 |
8 |
8 |
8 |
5 |
|
Hour beginning at |
13 |
14 |
15 |
16 |
17 |
18 |
19 |
20 |
21 |
22 |
23 |
24 |
|
|
Number of staff required |
5 |
5 |
5 |
8 |
8 |
8 |
9 |
10 |
10 |
10 |
10 |
8 |
|
Each staff must work in 6 consecutive hours. The salary per hour is $35. Determine how many staff should start working at the beginning of ith hour to minimize the total cost:
a) Formulate the problem as a linear programming model. Write down the model and explain it.
b) Solve the model in Excel and present the results and interpret them.
c) If it is possible to ask a staff to stay extra 2 hours with salary of $45 per hour. Formulate the problem, write the mathematical model and explain it.
d) Solve the model written in part c and explain the solution.
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