Problem 5 (20pts). (World Cup Market) Before one World Cup championship, there are 5 types of securities available for sale. The price of each share of the security is xed and the payoff of it will be contingent on the outcome of the outcome of the world cup. The information of the 5 securities are shown in Table 1. Here, for example, Security 1's payoff is 1 if either Argentina, Brazil, or England wins the world cup, and the payoff is 0 if Germany or Spain wins. The Share Limit is the maximum number of shares one can purchase, and Price is the current purchasing price per share of each security. Table 1: Payoff matrix 1. Assume that short is not allowed, that is, one can only buy shares but not sell. For mulate the problem as a linear program to decide how many shares of each security to purchase so as to maximize the worstcase (minimum) payoff1 when the game is nally realized. You can denote 7r = (0.8,0.3,0.4, 0.7, 0.6)T, q = (8, 5, 7, 8, 5)T and l 11 0 0 0 0 0 l 1 A: 1 0 1 0 l l l 1 1 0 0 l 0 1 1 For simplicity, the decision variables may take oat values