Use Matlab Optimization Methods, and Dimensional Plotting: Reference Chapter 7 of Applied Numerical Methods of MatLab for Engineers and Scientists.

Dissolved oxygen is frequently compromised downstream of waste-water treatment plants. The following equation estimates oxygen downstream of a plant: k,L k t 1-e -ka where A oxygen concentration (mg/L), As saturated oxygen concentration, t travel time (d), Lo biochemical oxygen demand at the mixing point, kd decomposition rate of BOD (d-1), ks settling rate (d-1) ka F reaeration rate (d-1), and Sb sediment oxygen demand (mg/L/d). Suppose you have the following parameters: As 10 mg/L, Lo 50 mg/L, kd 0.1 d-1, ks 0.04 d-1, ka 0.65 d-1, and Sb 1 mg/L/ Determine the critical time and concentration for observed sag in dissolved oxygen while oxygen is initially consumed faster than reaeration of oxygen into the stream