I'm not familiar with linear programming, but here is what I'd say: (since is the number of dollars spent to buy francs) and . Maximize subject to the constraints .
(By the way, euros would be more up-to-date than francs)
A man deals with French currency (the franc) and American currency (the dollar). At midnight, he can buy francs by paying dollars per franc and dollars by paying francs per dollar. Let and . Assume that both types of transactions take place simultaneously, and the only constraint it that at the man must have a nonnegative number of francs and dollars.
(a) Formulate an LP that enables the man to maximize the number of dollars he has after all transactions are completed.
Let where is the number of dollars the man has before the transaction. Similarly, let where is the number of francs the man has before the transaction. So is this the correct LP formulation:
maximize subject to constraints that . We can solve this right? This formulation allows for the man to not enter any transaction, right?