2. [20 points] A large drug company must determine how many sales representatives to assign to each of four sales districts to minimize costs. The cost of having $n$ representatives in a district is $(\$ 88,000+\$ 80,000 n)$ per year. If a representative is based in a given district, the time it takes to make a visit to a potential customer is given in Table 1 (times are in hours). Each representative can work up to 160 hours per month. Each month, the number of visits given in Table 2 must be made in each district. A fractional number of representatives is not permissible. Table 1: Hours per call \begin{tabular}{c||CCCC) \multicolumn{1}{c}}{ Representative's Base District } & \multicolumn{4}{c}{ Sales Visit District) \hline & 1 & 2 & 3 & 4 \hline 1 & 1 & 4 & 5 & 7 2 & 4 & 1 & 3 & 5 1 3 & 5 & 3 & 1 & 2 4 & 7 & 5 & 2 & 1 \end{tabular] Table 2: Required number of visits per month \begin{tabular}{cc) District & Number of visits \hline 1 & 50 2 & 80 3 & 100 4 & 60 \end{tabular) S.P.PB. 252