Homework Assignment 3
商科作业代写 The board of directors of Serious Cybernetics Company is considering 7 large capital investments. Each investment can be made only once.
Problem 1 (30 points) 商科作业代写
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 profits of the 7 potential investments are given in the table below (millions).
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 first 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 profit. What investments should Serious Cybernetics make?
Problem 2 (35 points) 商科作业代写
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.
The following players from other teams are available in the open market.
You want to improve your team, but you don’t have any extra money to use in recruiting new players. You can, however, sell the rights to some of your players in order to raise money to purchase the rights to other players. You want to have the same number of players in each section (4 defenders, 4 midfielders and 2 strikers) after your trades.
Assume that if you don’t touch a given section of the team (defense, midfield or attack),then that section will perform 5% better (in all skills) than predicted by the stats because the players will already be familiar with each other’s playing style. 商科作业代写
Are there any trades that you could make that, without adding any new money, would create a team better in defense, passing and shooting than the current roster? Assume that all players’ skills count (for example, the average shooting skills of the team is the average of all players, not just the strikers’ shooting skills). Do not pick a trade that would improve the team on one skill, while hurting it on others. When you consider whether the new roster is better in a given skill, don’t forget to take into account the 5%familiarity bonus.
Problem 3 (35 points)
A typhoon just hit the Philippines with devastating consequences. You work for a local disaster relief organization and you need to act fast to save lives. The following are the immediate needs of the different affected islands (all measured in tons). If you bring more supplies than listed below, the extra supplies will not help save lives.
You have 6 boats at your disposal in the island of Luzon, which was not affected by the typhoon. Each boat can transport 10 tons of supplies. You have plenty of food, drinking water and medical equipment in Luzon, so there is no constraint regarding what you can load on the boats. 商科作业代写
A ton of food can save 100 lives. A ton of drinking water can save 200 lives. A ton of medical equipment can save 500 lives.a) (15 points) You are planning to send 2 boats to Bohol, 2 boats to Cebu and 2 boats to Leyte. What supplies should you load on each boat in order to maximize the number of lives saved? Formulate a linear optimization problem to answer this question.
b) (20 points) Consider now the general problem. You can decide how many boats to send to each island and what supplies to load on each of those boats. Formulate a linear integer optimization to decide how many boats to send to each island and what supplies to load onto the boats in order to maximize the number of lives saved.
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