For each of the following three problems, (a) Write the linear programming (LP) model that could be used to find the best solution (clearly define the decision variables and any other notations you use in your model, show the necessary set of algebraic expressions for the constraints and the objective function, and label the units and the purpose of each constraint and the objective function) (b) Use an LP software to solve your model and submit the input file you used (c) Write out the final solution Problem 3: 5-32. Four cities discharge wastes containing biochemical oxygen demand (BOD) into a river. The cities are far enough apart that combined treatment is not practical. However, a regional authority wishes to minimize the overall costs of treating the wastes so water quality requirements in the river are met. Different limitations are put on the allowable BOD load in the river because of different expected uses of the water. The BOD load in the river above City 1 is 0.0003lb/ft3. Removal of BOD by natural processes in the river follows an exponential decay function Ri,i+1=exp(kti,i+1) in which RL,i+1= the fraction of BOD remaining after passage from City i to City i+1, k= BOD exertion rate, and ti,i+1= time of river travel from City i to City i+1. Streamflow is to be considered to be constant between cities. The maximum efficiency of BOD removal at any of the cities is 85%. Formulate a model that could be used to determine the minimum cost method of achieving the required river quality. Pertinent data are given below