Please answer the questions from part (d-h)

Project Pickings Tazer, a pharmaceutical manufacturing company, entered the pharmaceutical market 12 years ago with the introduction of six new drugs. Five of the six drugs were simply permutations of existing drugs and therefore did not sell very heavily. The sixth drug, however, addressed hypertension and was a huge suc- cess. Since Tazer had a patent on the hypertension drug, it experienced no competition, and profits from the hypertension drug alone kept Tazer in business. During the past 12 years, Tazer continued a moderate amount of research and development, but it never stumbled upon a drug as successful as the hypertension drug. One reason is that the company never had the motivation to invest heavily in innovative research and development. The company was riding the profit wave generated by its hypertension drug and did not feel the need to commit significant resources to finding new drug breakthroughs. Now Tazer is beginning to fear the pressure of competition. The patent for the hypertension drug ex- pires in five years,' and Tazer knows that once the patent expires, generic drug manufacturing compa- nies will swarm into the market like vultures. Historical trends show that generic drugs decrease sales of branded drugs by 75 percent. Tazer is therefore looking to invest significant amounts of money in research and development this year to begin the search for a new breakthrough drug that will offer the company the same success as the hyper- tension drug. Tazer believes that if the company begins extensive research and development now, the prob- ability of finding a successful drug shortly after the expiration of the hypertension patent will be high. As head of research and development at Tazer, you are responsible for choosing potential projects and assigning project directors to lead cach of the projects. After researching the needs of the market, ana- lyzing the shortcomings of current drugs, and interviewing numerous scientists concerning the promis- ing areas of medical research, you have decided that your department will pursue five separate projects, which are listed below: Project Up: Develop a more effective antidepressant that does not cause serious mood swings. Project Stable: Develop a drug that addresses manic-depression. Project Choice: Develop a less intrusive birth control method for women. Project Hope: Develop a vaccine to prevent HIV infection. Project Relcase: Develop a more effective drug to lower blood pressure. For each of the five projects, you are only able to specify the medical ailment the research should address since you do not know what compounds will exist and be effective without research. You also have five senior scientists to lead the five projects. You know that scientists are very tem- peramental people and will only work well if they are challenged and motivated by the project. To ensure that the senior scientists are assigned to projects they find motivating, you have established a bidding sys- tem for the projects. You have given each of the five scientists 1,000 bid points. They assign bids to each project, giving a higher number of bid points to projects they most prefer to lead. The following table provides the bids from the five senior scientists for the five individual projects: Dr. Kvaal Dr. Zuner Dr. Rollins Project Project Up Project Stable Project Choice Project Hope Project Release 100 400 200 200 100 0 200 800 0 0 Dr. Tsai 100 100 100 100 600 Dr. Mickey 267 153 99 451 30 100 33 33 34 800 You decide to evaluate a variety of scenarios you think are likely. a. Given the bids, you need to assign one senior scientist to cach of the five projects to maximize the preferences of the scientists. What are the assignments? b. Dr. Rollins is being courted by Harvard Medical School to accept a teaching position. You are fight- ing desperately to keep her at Tazer, but the prestige of Harvard may lure her away. If this were to hap- pen, the company would give up the project with the least enthusiasm. Which project would not be done? c. You do not want to sacrifice any project since rescarching only four projects decreases the probabil- ity of finding a breakthrough new drug. You decide that either Dr. Zuner or Dr. Mickey could lead two projects. Under these new conditions with just four senior scientists, which scientists will lead which projects to maximize preferences? d. After Dr. Zuner was informed that she and Dr. Mickey are being considered for two projects, she de- cided to change her bids. Dr. Zuner's new bids for each of the projects are the following: Project Up: 20 Project Stable: 450 Project Choice: 451 Project Hope: 39 Project Release: 40 Under these new conditions with just four senior scientists, which scientists will lead which projects to maximize preferences? e. Do you support the assignments found in part d? Why or why not? f. Now you again consider all five scientists. You decide, however, that several scientists cannot lead cer- tain projects. In particular, Dr. Mickey does not have experience with research on the immune sys- tem, so he cannot lead Project Hope. His family also has a history of manic-depression, and you feel that he would be too personally involved in Project Stable to serve as an effective project leader. Dr. Mickey therefore cannot lead Project Stable. Dr. Kvaal also does not have experience with research on the immune system and cannot lead Project Hope. In addition, Dr. Kvaal cannot lead Project Re- lease because he does not have experience with research on the cardiovascular system. Finally, Dr. Rollins cannot lead Project Up because her family has a history of depression and you feel she would be too personally involved in the project to serve as an effective leader. Because Dr. Mickey and Dr. Kvaal cannot lead two of the five projects, they each have only 600 bid points. Dr. Rollins has only 800 bid points because she cannot lead one of the five projects. The following table provides the new bids of Dr. Mickey, Dr. Kvaal, and Dr. Rollins: Dr. Kvaal Dr. Rollins Project Project Up Project Stable Project Choice Project Hope Project Release Dr. Mickey 300 Can't lead 125 Can't lead 175 86 343 171 Can't lead Can't lead Can't lead 50 50 100 600 Which scientists should lead which projects to maximize preferences? g. You decide that Project Hope and Project Release are too complex to be led by only one scientist. Therefore, each of these projects will be assigned two scientists as project leaders. You decide to hire two more scientists in order to staff all projects: Dr. Arriaga and Dr. Santos. Because of religious rea- sons, neither of them want to lead Project Choice and so they assign 0 bid points to this project. The following table lists all projects, scientists, and their bids. Kvaal Zuner Tsai Santos Project Up Stable Choice Hope Release 86 343 171 Can't lead Can't lead Rollins Can't lead 50 0 200 800 0 0 Mickey 300 Can't lead 125 Can't tead 175 100 100 100 100 600 Arriaga 250 250 0 250 250 50 111 1 0 333 555 100 600 Which scientists should lead which projects to maximize preferences? h. Do you think it is wise to base your decision in part g only on an optimal solution for a variant of an assignment