There are six operators (four men and two women). They all have different wage rates because of differences in their experience with computers and in their programming ability. The following table shows their wage rates, along with the maximum number of hours each can work each day.
| Operator | Wage rate | Maximum hours of availability | ||||
|---|---|---|---|---|---|---|
| Mon. | Tue. | Wed. | Thurs. | Fri. | ||
| K.C. | $6.00/hour | 6 | 0 | 6 | 0 | 6 |
| D.H. | $6.10/hour | 0 | 6 | 0 | 6 | 0 |
| H.B. | $5.90/hour | 4 | 8 | 4 | 0 | 4 |
| S.C. | $5.80/hour | 5 | 5 | 5 | 0 | 5 |
| K.S. | $6.80/hour | 3 | 0 | 3 | 8 | 0 |
| N.K. | $7.30/hour | 0 | 0 | 0 | 6 | 2 |
Because of a tight budget, the director has to minimize cost. His decision is that the operators with the highest wage rates should work the least possible number of hours, except this number should not be as low as to impair his or her knowledge of the operation. This level is set arbitrarily at 8 hours per week for the male operators and 7 hours per week for the female operators (K.S., N.K.).
The computer facility is to be open for operation from 8 a.m. to 10 p.m. Monday through Friday with exactly one operator on duty during these hours. On Saturdays and Sundays, the computer is to be operated by other staff.
Formulate a linear programming model so the director can determine the number of hours he should assign to each operator on each day.