At the beginning of the fall semester, the director of the computer facility of
ID: 2454830 • Letter: A
Question
At the beginning of the fall semester, the director of the computer facility of a certain university is confronted with the problem of assigning different working hours to his operators. Because all the operators are currently enrolled in the university, his main concern is to make certain that the operators' working times are not so excessive that they would interfere with study times.
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.
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.
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 2Explanation / Answer
Let us assign variables as below for the number of hours to be worked by each operator.
Then the equations are as below
Minimize 6A + 6.1B + 5.9C + 5.8D + 6.8X + 7.3Y
A,B,C,D < 7 and X,Y < 8 since this is the level set for male and female workers
A+B+C+D+X+Y < 14 since this is the maximum availability of computer per day.
Operator Wage rate Maximum hours of availability Variablefor Hours Mon. Tue. Wed. Thurs. Fri. MaxLimit K.C. $6.00/hour A 6 0 6 0 6 8 D.H. $6.10/hour B 0 6 0 6 0 8 H.B. $5.90/hour C 4 8 4 0 4 8 S.C. $5.80/hour D 5 5 5 0 5 8 K.S. $6.80/hour X 3 0 3 8 0 7 N.K. $7.30/hour Y 0 0 0 6 2 7Related Questions
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