$**$Please include the calculation steps in your answers to show your work $($not just the final results$).$

Q $1(60$ pts$.).$ You were asked to estimate the environmental impact associated with water consumption per capita per day in a small city with $100,000$ population. The water supply in the city is provided by a local water treatment plant. You visited the water treatment plant a few times to understand how the water is treated and distributed to consumers. After your plant visits, you completed a flow chart including all the processes for water treatment$/$distribution $($Figure $1)$ and related data $($Figure $2).$ You also searched references to compile data related to material $($coagulant$)$ and energy $($electricity$)$ used for water treatment and distribution $($Figure $3).$

Use the LCA matrix method you learned in this course to calculate the environmental impact $($inventory$)$ of water consumption per capita per day in the small city:

Q $1-1.$ What water amount is consumed per capita per day $(5$ pts$.)$; using this water amount to define the demand vector $\backslash (\backslash$mathrm$\{$f$\}(5\backslash$mathrm$\{$pts$\}\backslash ).).$

Q $1-2.$ Define the technical matrix A$.(20$ pts$.)$

Q $1-3.$ Calculate the scaling matrix s$.(15$ pts$.)$

Q $1-4.$ Define the environmental matrix B and calculating environmental impact $($inventory$)$ g$.(15$ pts $)$

Page $1$ of $3$ Figure $2$: Data for water treatment and distribution