6 Five male characters (Billie, John, Fish, Glen, and Larry) and five female characters (Ally, Georgia, Jane, Rene, and Nell) from Ally McBeal are marooned on a desert island. The problem is to determine what percentage of time each woman on the island should spend with each man. For example, Ally could spend 100% of her time with John or she could play the field" by spending 20% of her time with each man. Table 55 shows a "happiness index" for each potential pairing of a man and woman. For example, if Larry and Rene spend all their time together, they earn 8 units of happiness for the island. a Play matchmaker and determine an allocation of each man and woman's time that earns the maximum to- tal happiness for the island. Assume that happiness earned by a couple is proportional to the amount of time they spend together. b Explain why the optimal solution to this problem will, for any matrix of "happiness indices," always in- volve each woman spending all her time with one man. TABLE 55 Ally Georgia Jane Rone Nell 8 Bilie John Fish Larry