Problem $1(30$ Points$)$: You and your engineering team are responsible for designing a new sewage treatment plant for the city of Terre Haute. The following twelve objectives have been established for consideration when designing the new treatment plant: architectural appearance $(k=0\mathrm{.}10),$ design$/$planning fees $(k=0\mathrm{.}20),$ environmental impact $(k=0\mathrm{.}20),$ construction cost $(k=0\mathrm{.}40),$ discharge water quality $)=(0\mathrm{.}40,$ public opinion $)=(0\mathrm{.}50,$ discharge location $)=(0\mathrm{.}50,$ government bylaws $)=(0\mathrm{.}40,$ noise$/$smell $)=(0\mathrm{.}20,$ operating costs $)=(0\mathrm{.}40,$ distance to sewage sources $)=(0\mathrm{.}50,$ and power requirements $)=(0\mathrm{.}20.$ Make the criteria tree and then use its w to calculate the relative weighting factors for each attribute and enter them in the following table. Then, calculate the total weighted value for each concept design $(A,B,$ and $C)$ and circle the best concept design.