Anderson's Law Office just received four new legal cases from its clients. Each case is about different legal issues, divorce, bankruptcy, labor and employment, and criminal law. Anderson is assigning these four legal cases to six attorneys in his office. He reviews the past five years' records of each attorney and concludes the winning probabilities of each attorney to each case as follows:
| ATTORNEY/CASE |
DIVORCE |
BANKRUPTCY |
LABOR AND EMPLOYMENT |
CRIMINAL LAW |
| 1 |
85% |
70% |
30% |
20% |
| 2 |
35% |
75% |
85% |
15% |
| 3 |
50% |
60% |
25% |
90% |
| 4 |
10% |
55% |
65% |
70% |
| 5 |
45% |
95% |
30% |
65% |
| 6 |
5% |
50% |
60% |
80% |
Anderson is trying to assign these four cases with the following restrictions:
(1) Each attorney should be assigned to at most one case.
(2) One and only one attorney should be assigned to each case.
(3) Attorneys 1 and 6 must be assigned a case.
(4) Attorney 5 cannot be assigned to the Bankruptcy case because of a confliction of interest.
Formulate an integer program model to maximize the total winning probability.