Currency Conversion Problem
We have currently cash reserves in six different currencies in the amounts given in the second column of the following table (in millions). Our objective is to convert these amounts in order to have reserves at least equal to the amounts given in the last column of the table. Initial Position 5 70 3 15 2 7 8 Desired Position 8 25 5 4 3 3 12
U.S. $ ¥en Euro Can $ U.K. £ Aust $ SFranc The conversion rates are as follows: Cross Rates 20-Jan-05 U.S. $ ¥en Euro Can $ U.K. £ Aust $ SFranc U.S. $ 1 0.009742 1.2999 0.8197 1.8737 0.7696 0.8445
Currency Purchased
¥en 102.6500 1 133.4347 84.1462 192.3353 78.9994 86.6903
Currency Sold Euro Can $ U.K. £ 0.7693 1.2200 0.5337 0.007494 0.011884 0.005199 1 1.5857 0.6938 0.6306 1 0.4375 1.4414 2.286 1 0.5920 0.939 0.4107 0.6497 1.030 0.4507
Aust $ 1.2994 0.012658 1.6891 1.0651 2.435 1 1.097
SFranc 1.1842 0.011535 1.5392 0.9707 2.2186 0.9113 1
The numbers in this table should be read as follows: to buy 1 U.S.$ for Japanese ¥en requires 102.56 ¥en (the element in the first row and the second column), 1 U.S.$ costs 0.7693 Euro, etc. If we want to buy 1 Japanese ¥en for U.S.$ we have to pay $0.009742 (the element in the ¥en row and U.S.$ column), etc. Design the conversion plan to meet the desired goals and to maximize the U.S.$ value of the obtained positions.