Problem 6. (Currency Conversion) Current cash reserves and their desired p0sition in six different curren- cies (in millions) are as follows. Initial Position Desired Position U.S.S Yen Euro Can.S G.B. Aust.S Swiss Franc 5 8 70 100 3 5 15 4 2 7 5 12 We want to convert the initial position amounts so that we have reserves at least equal to the amounts in the desired position. The conversion rates are presented in the second table. U.S.S Can.S G.B. 0.9902 0.6211 Yen uro Aust.S 0.9489 Swiss Franc U.S.S 76.925 1 0.7827 0.7091 Yen Euro Can.$ G.B. 0.013 1 0.0092 0.0129 0.0081 0.0133 0.0102 1.4102 108.4797 1 1.3963 0.8759 1.3381 1.1038 1.0099 77.6903 0.7162 1 0.6273 0.9583 0.7905 1.61 123.8485 1.1417 0.7473 1.5941 1.5277 1.2602 Aust.S 1.0538 81.0784 1.0435 0.6546 0.8249 Swiss Franc 1.2776 98.2759 0.9059 1.265 0.7935 1.2123 1 The mumbers in this table should be understood this way: buying 1 U.S. dollar for Japanese Yen requires 76.925 Y, 1 U.S. dollar costs 0.7091, etc. In order to buy 1 Japanese Yen for U.S. dollars we need to pay $0.013, etc. Find the optimal conversion plan to satisfiy the goals and to maximize the value of U.S $ of the new position