QNT$2020-$BTRA Project #$21$ QNT$2020-$BTRA $($Fall $2024)$ PROJECT #$2$ Science Projects A pharmaceutical company named, Forefront Pharmaceutical, entered the pharmaceutical industry $25$ 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 well. The sixth drug, however, addressed hypertension and was huge success. Since Forefront had a patent on the hypertension drug, it experienced no competition, and profits from the hypertension drug alone kept Forefront in business. Pharmaceutical patens remain in force for $20$ years, so this one has five more years before it expires. During the past $25$ years, Forefront 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 o 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 Forefront is beginning to fear the pressure of competition. Forefront knows that once the patent expires in five years, generic drug manufacturing companies will swarm into the market like vultures. Historical trends show that generic drugs decrease sales of branded drugs by $75\%.$ Forefront 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 hypertension drug. Forefront believes that if the company begins extensive research and development now, the probability of finding a successful drug shortly after the expiration of the hypertension patent will be high. As head of research and development at Forefront, you are responsible for choosing potential projects and assigning project directors to lead each of the projects. After researching the needs of the market, analyzing the shortcomings of current drugs, and interviewing numerous scientists concerning the promising areas of medical research, you have decided that your department will pursue five separate projects, which are listed below: Project Happy: 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 Release: 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 temperamental 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 QNT$2020-$BTRA Project #$22$ have established a bidding system 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. Projects Dr$.$ Lee Dr$.$ Santos Dr$.$ George Dr$.$ Langford Dr$.$ Chen Project Happy $1000100267100$ Project Stable $40020010015333$ Project Choice $2008001009933$ Project Hope $200010045134$ Project Release $100050030800$ You decide to evaluate a variety of scenarios you think are likely to play out. a$)$ Give the bids, you need to assign one senior scientist to each of the five projects to maximize the preferences of the scientists. What are the assignments? b$)$ Dr$.$ Chen is being courted by Yale Medical School to accept a teaching position. You are fighting desperately to keep her at Forefront, but the prestige of Yale may lure her away. If this were to happen, the company would give up the project with the least enthusiasm. Which project would not be done? c$)$ If Dr$.$ Chen leaves, you do not want to sacrifice any project since researching only four projects decreases the probability of finding a breakthrough new drug. You decide that either Dr$.$ Santos or Dr$.$ Langford 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$.$ Santos was informed that she and Dr$.$ Langford are being considered for two projects, she decided to change her bids. Dr$.$ Santos$$ new bids for each of the projects are shown below. Project Happy: $20$ 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$)$