Problem 2 (40 points) Assume that there are two sites along a stream, i=1, 2, at which industrial waste is discharged to the river. Current discharge levels are W; and W2 at these sites. Industrial waste signicantly deteriorates water quality in the river, and water quality is being monitored in sites 2 and 3. Currently, without any wastewater treatment, the water quality at each of sites 2 and 3 (q: and qg) is less than the minimum desired, Q2, Q3, respectively. At each site i, there is a waste treatment option available. R i is the 'acrion of waste discharge (WE) being treated at site 1'. The cost per unit of waste treated is 6:. For each unit of waste treated at site i upstream of site j, the quality improves by Ag. W1 Stream W2 Part 2-1) Formulate a linear programming model to determine how much treatment is required at sites 1 and 2 that meets the standards at a minimum total cost. Specify the objective function, decision variable(s) and the constraint(s). Part 2-2) Solve the optimization problem given the following data: W; =100, W2 =75, A12 =1/20, A13 =l/40,A23 =1/30, qz =3, (13 =1 , Q2 =6, Q3 =4, CI =100, 02 =50. Part 2-3) Find the shadow price for the water quality constraints. How do you interpret the shadow price for each of the water quality constraints? Part 2-4) While keeping all the other variables as stated in part 2-2, how does the optimal solution changes for different values of c1 and c2 ? Hint: Use the graphical approach and find a relationship between c:1 and c2