A small engineering consulting firm is establishing a plan for next year. The director and the three partners need to prioritize the eight projects. The expected profit for each project is given in the following table together with the number of person$-$days required to prepare each project. Another measure included is the computing resource measured as the computer processing unit $($CPU$)$ time $($in hours$).$ You have been tasked to evaluate which projects they ought to pursue based on efficiency. Given the sample data below, you plan to construct a data envelopment analysis $($DEA$)$ model:

Project Profit $($in million $)12\mathrm{.}1$

$20\mathrm{.}5$

$33$

$425161\mathrm{.}570\mathrm{.}681\mathrm{.}8$

person$-$days CPU time $($hours$)550200$

$400150300400350450450300$

$500150350200200600$

$1.$ Which measures would you regard as inputs and outputs, respectively? Please provide your justification. $(5$ marks$)$

$2.$ Conductdataenvelopmentanalysis,explainwhattypeofDEAmodelisselectedanddescribe the project you regard as $$efficient$$ and $$inefficient$,$ respectively. $(8$ marks$)$

$3.$ Which project would you recommend and why? $(7$ marks$)$

$4.$ In what ways can you improve on your recommendation? You are free to openly source for other datasets $($or create one$)$ and justify the new set of input and output measures before conducting another data envelopment analysis.

Elaborate on your recommendations and solutions. $(10$ marks$)$

$5.$ Assuming that you have to consider the project from a different industry in your analysis and you can have any data and measurement at your disposal, what would be the ideal steps taken to ensure that the projects from different industries are comparable?