Problem 1 (30 points) The board of directors of Serious Cybernetics Company is considering 7 large capital investments. Each investment can be made only once. The capital requirements and estimates prots of the 7 potential investments are given in the table below (millions). Investment Est. Prot Req. Opportunity Capital 1 17 43 2 10 28 3 4 5 6 7 There total amount of capital available is $100M. Investment opportunities 1 and 2 are mutually exclusive. Investment opportunities 3 and 4 are also mutually exclusive. Furthermore, neither 3 nor 4 can be undertaken unless one of the rst two opportunities is undertaken. Projects 5 and 7 have synergies such that if both projects are undertaken, you expect to obtain an extra 5M in prot. What investments should Serious Cybernetics make? Problem 2 (35 points) You are the manager of a soccer team and you need to decide which players to trade for the next season. The following is your current roster except for the goalkeeper. The list below lists the players' skills and current market value. m Defense Skills Passing Skills Shooting Skills Defendem n- _-W Defender C 0.6 million Defender D 1 million Midelder E 3 million Midelder F 1 million Midelder G 1.8 million Midelder H 1.2 million 8 million 1.5 million DJ |\\ -- -_ -_- - _- w WEI-\"\" The following players from other teams are available in the open market