LP Modeling

Bankruptcy Problem

Albert, Bill, Charles, David, and Edward have gotten into a bind. After a series of financial transactions, they have ended up each owing some of others huge amounts of money. In fact, near as the lawyers can make out, the debts are as follow:

Debtor Creditor Amount ($millions)

A E 10

A C 3

B A 5

C B 6

C D 4

D A 4

E C 7

E D 3

The question is, who is bankrupt? We will say that a person is bankrupt if there is no possible transfer of funds among the people such that completely pays off his obligations. For instance, Albert is bankrupt since he owes 13, and is only owed 9. Edward is bankrupt as well since he owes 10 and, although he is owed 10, this debt is owed to him by Albert who can pay at most 9.

Your job:

1) Formulate the problem of determine whether Bill is bankrupt, as a linear program.

2) Modify your formulation to determine who of the others is bankrupt.