At the beginning of the fall semester, the director of the computer facility of bradley university is confronted with the problem of assigning different working hours to her operators. because all the operators are currently enrolled in the university, her main concern is to make certain that the operator's working times are not so excessive that they would interfere with study times.

there are six operators. 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 that each can work each day of the week.

maximum hours of availability
operators wage rate monday tuesday wednesday thursday friday
a $6.00/hr 6 0 6 0 6
b $6.10/hr 0 6 0 6 0
c $5.90/hr 4 8 4 0 4
d $5.80/hr 5 5 5 0 5
e $6.80/hr 3 0 3 8 0
f $7.30/hr 0 0 0 6 2
because of a tight budget, the director has to minimize cost, but each operator should be able to work at least 7 hours per week. each day of the week, the computer facility must be open for 8 hours per day. formulate a linear programming model so that the director can determine the number of hours she should assign to each operator on each day. do not attempt to solve the model.