Orchid Biotech Company is evaluating several different development projects for experimental drugs. Although the cash flows are difficult to$$ forecast, the company has come up with the following estimates of the initial capital requirements and NPVs for the$$ projects:

Project Number Initial Capital Number of Research Scientists NPV

$1$ $$102$ $$10\mathrm{.}1$

$2$ $$153$ $$19\mathrm{.}0$

$3$ $$154$ $$22\mathrm{.}0$

$4$ $$203$ $$25\mathrm{.}0$

$5$ $$3012$ $$60\mathrm{.}2$

Given a wide variety of staffing$$ needs, the company has also estimated the number of research scientists required for each development project$($all cost values are given in millions of$$ dollars$).$

a$.$ Suppose that Orchid has a total capital budget of $ $60$ million. How should it prioritize these$$ projects? $($Round to two decimal$$ places.$)$

The profitability index for Project $1$ is $\_\_\_\_\_$

The profitability index for Project $2$ is $\_\_\_\_\_$

The profitability index for Project $3$ is $\_\_\_\_\_$

The profitability index for Project $4$ is $\_\_\_\_\_$

The profitability index for Project $5$ is $\_\_\_\_\_$

Based on the profitability$$ index, how should Orchid prioritize these$$ projects?

Selected first: $\_\_\_\_\_(1,2,3,4$ or $5)$

Selected second: $\_\_\_\_\_(1,2,3,4$ or $5)$

Selected third: $\_\_\_\_\_(1,2,3,4$ or $5)$

b$.$ Suppose that Orchid currently has $12$ research scientists and does not anticipate being able to hire more in the near future. How should Orchid prioritize these$$ projects? $($Round to one decimal$$ place.$)$

The $$NPV$/$headcount ratio for Project $1$ is $\_\_\_\_\_.$

The $$NPV$/$headcount ratio for Project $2$ is $\_\_\_\_\_.$

The $$NPV$/$headcount ratio for Project $3$ is $\_\_\_\_\_.$

The $$NPV$/$headcount ratio for Project $4$ is $\_\_\_\_\_.$

The $$NPV$/$headcount ratio for Project $5$ is $\_\_\_\_\_.$ Based on the NPV$/$headcount $$ratio$,$ how should Orchid prioritize these$$ projects?

Selected first: $\_\_\_\_\_(1,2,3,4$ or $5)$

Selected second: $\_\_\_\_\_(1,2,3,4$ or $5)$

Selected third: $\_\_\_\_\_(1,2,3,4$ or $5)$

Selected fourth: $\_\_\_\_\_(1,2,3,4$ or $5)$