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 success. Since Tazer had a patent on

the hypertension drug, it experienced no competition, and profits from the hyperten$-$

sion drug alone kept Tazer in business.

During the past $12$ years, Tazer continued a moderate amount of research and de$-$

velopment, 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 innova$-$

tive 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 find$-$

ing new drug breakthroughs.

Now Tazer is beginning to fear the pressure of competition. The patent for the hy$-$

pertension drug expires in $5$ years, ${?}^1$ and Tazer knows that once the patent expires,

generic drug manufacturing companies will swarm into the market like vultures. His$-$

torical trends show that generic drugs decreased 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 hypertension drug. Tazer believes that if the com$-$

pany begins extensive research and development now, the probability of finding a suc$-$

cessful 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 each of the projects. After re$-$

searching 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 Up

Project Stable

Project Choice

Project Hope

Project Release

Develop an antidepressant that does not cause serious mood swings.

Develop a drug that addresses manic$-$depression.

Develop a less intrusive birth control method for women.

Develop a vaccine to prevent HIV infection.

Develop a more effective drug to lower blood pressure.

$\text{'}$In general, patents protect inventions for $17$ years. In $1995,$ GATT legislation extending the protection given

by new pharmaceutical patents to $20$ years became effective. The patent for Tazer's hypertension drug was

issued prior to the GATT legislation, however. Thus, the patent only protects the drug for $17$ years.For each of the five projects, you are only able to specify the medical ailment the re$-$

search should address, since you do not know what compounds will exist and be ef$-$

fective without research.

You also have five senior scientists to lead the five projects. You know that scien$-$

tists are very temperamental people and will work well only 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 system for the projects. You have given

each of the five scientists $1000$ 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 pro$-$

vides the bids from the five individual senior scientists for the five individual projects:

You decide to evaluate a variety of scenarios you think are likely.

$($a$)$ Given the bids, you need to assign one senior scientist to each of the five projects to maxi$-$

mize 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 fighting desperately to keep her at Tazer, but the prestige of Harvard 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$)$ 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$.$ 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 proj$-$

ects, she decided to change her bids. The following table shows Dr$.$ Zuner's new bids for

each of the projects:

Under these new conditions with just four scientists, which scientists will lead which proj$-$

ects to maximize preferences?

$($e$)$ Do you support the assignment found in part $($d$)?$ Why or why not?

$($f$)$ Now you again consider all five scientists. You decide, however, that several scientists

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