Formulate a data-independent linear program model for the following problem.

Countribank's International Fund managers job is to determine how the banks current holdings of dollars, pounds, marks, and yen should be adjusted to meet the days currency needs. Today the exchange rates between the various currencies are given in Table 1 . For example, one dollar can be converted to 0.58928 pounds, or one pound can be converted to 1.697 dollars. At the beginning of Decision Variables: the day, Countribank has the currency holdings given in Table 2. At the end of the day, Countribank - xij : amount of currency i converted to currency j (in Billions) must have at least the amounts of each currency given in Table 3 . The manager's goal is to each day - yj : amount of currency j at the end of the day (in Billions) transfer funds in a way that makes currency holdings satisfy the previously listed minimums, and maximizes the dollar value of the currency holdings at the end of the day. To figure out the dollar value of, say, one pound, average the two conversion rates. Thus, one pound is worth approximately 21.697+0.589281=1.696993dollars Table 1: Exchange rates Table 2 : Initial currency holdings Table 3: Final currency target amounts