The Indiana University Business School has two rooms that each seat 50 students, one room that seats 100 students, and one room that seats 150 students. Classes are held five hours a day. The four types of requests for rooms are listed in Table 37. The business school must decide how many requests of each type should be assigned to each type of room. Penalties for each type of assignment are given in Table 38. An X means that a request must be satisfied by a room of adequate size. Formulate an IP whose solution will tell the business school how to assign classes to rooms in a way that minimizes total penalties AND SOVE IT USING CPLEX

TABLE 36 \begin{tabular}{lccc} \hline Subsidiary & Average Payroll & Reserve & Estimated Payroll \\ \hline 1 & 300 & 400 & 350 \\ 2 & 600 & 510 & 400 \\ 3 & 800 & 600 & 500 \\ \hline \end{tabular} TABLE 37 \begin{tabular}{lccc} \hline Type & Size Room Requested (Seats) & Hours Requested & Number of Requests \\ \hline 1 & 50 & 2,3,4 & 3 \\ 2 & 150 & 1,2,3 & 1 \\ 3 & 100 & 5 & 1 \\ 4 & 50 & 1,2 & 2 \\ \hline \end{tabular} TABLE 36 \begin{tabular}{lccc} \hline Subsidiary & Average Payroll & Reserve & Estimated Payroll \\ \hline 1 & 300 & 400 & 350 \\ 2 & 600 & 510 & 400 \\ 3 & 800 & 600 & 500 \\ \hline \end{tabular} TABLE 37 \begin{tabular}{lccc} \hline Type & Size Room Requested (Seats) & Hours Requested & Number of Requests \\ \hline 1 & 50 & 2,3,4 & 3 \\ 2 & 150 & 1,2,3 & 1 \\ 3 & 100 & 5 & 1 \\ 4 & 50 & 1,2 & 2 \\ \hline \end{tabular}