00:01
In this question, we have been given that at the beginning of the fall semester, the director of the computer facility is confronted with the problem of assigning different working hours to his operator.
00:14
We need to formulate a linear programming model that the director can use to determine the number of hours he should assign to each of the operators.
00:24
Here we have been given six operators.
00:27
So we have to formulate one linear programming problem.
00:30
So first i will define what are the decision variables.
00:36
So this is xij, which means that it represents hours operator i is assigned to work on day j.
00:56
And this is for all i going from 1 till 6, where 1 represents the first operator, which is kc and so on.
01:12
The last operator will be represented by 6 and j is going from 1 till 5, where 1 corresponds to the monday and similarly 5 will correspond to friday.
01:30
These are the working days.
01:33
So in this question, we need to minimize z.
01:38
So this is the objective function i'm writing is equals to 6 times x 1 1.
02:13
Plus x 4 2 plus x 4 3 plus x 4 5, then 6 .8 times x 5 1 x 5 3 and x 5 4 plus 7 .3 times x 6 4 plus x 6 5.
02:36
So this will, this is what the assignment of hours to the operator and it is subjected to the following constraint.
02:50
So the constraint will be based on the maximum number of hours available each day.
02:55
So for the first operator on the first day, it is less or equals to 6.
03:01
For the second operator on the second day, less or equals to 6...