*** Need this solution in manual formulation, showing decision variables, constraints and the equations, pls do not use excel for the answer***

IIM Kozhikode maintains a powerful mainframe computer for research use by its faculty, Ph.D. students, and research associates. During all working hours, an operator must be available to operate and maintain the computers, as well as to perform some programming services. Mr Sansar Saxena, an IIMK alumnus and the director of the computing facility, oversees the operation. It is now the beginning of the fall semester, and Saxena is confronted with the problem of assigning different working hours to his operators. Because all the operators are currently enrolled in the university, they are available to work only a limited number of hours each day, as shown in the following table. There are 6 operators and all have different wage rates because of differences in their experience with computers. The above table shows their wage rates, along with the maximum number of hours that each can work each day. Each operator is guaranteed a certain minimum number of hours per week that will maintain an adequate knowledge of the operation. This level is set arbitrarily at 8 hours per week. The computing facility is to be open for operation from 8 am to 10 pm Monday through Friday with exactly one operator on duty during these hours. Because of a tight budget, Siva has to minimize the cost by determining the number of hours he should assign to each operator on each day. Help him develop a mathematical model to achieve the same.

\begin{tabular}{|c|c|c|c|c|c|c|} \hline & & \multicolumn{5}{|c|}{ Maximum hours of availability } \\ \hline Operators & Wage Rate & Monday & Tuesday & Wednesday & Thursday & Friday \\ \hline Lakshmi & $10/ hour & 6 & 0 & 6 & 0 & 6 \\ \hline Madhavi & $11 hour & 0 & 6 & 0 & 6 & 0 \\ \hline Ayushi & $9/ hour & 4 & 8 & 4 & 0 & 4 \\ \hline Netra & $8/ hour & 5 & 5 & 5 & 0 & 5 \\ \hline Abirami & $13/ hour & 3 & 0 & 3 & 8 & 0 \\ \hline Kavi & $12/ hour & 0 & 0 & 0 & 6 & 2 \\ \hline \end{tabular}