This is in Numerical Methods and Optimization all about using numerical methods ( Golden Search Method,Newtons Method in Optimization, Linear Programming Method). Provide clean and clear solutions. YOU MAY USE 2 METHODS thank you

7.29 The Streeter-Phelps model can be used to compute the dissolved oxygen concentration in a river below a point dis- charge of sewage (Fig. P7.29), kaLo 0 = 0s (ekat - e-( kathi) ) ka +ks - ka Sb (P7.29) (1 -e -katy 12 8 (mg/L) 0 0 5 10 15 20 1 (d) FIGURE P7.29 A dissolved oxygen "sag" below a point discharge of sewage into a river.where o = dissolved oxygen concentration (mg/L), of = oxygen saturation concentration (mg/L), / = travel time (d), L. = biochemical oxygen demand (BOD) concentration at the mixing point (mg/L), k. = rate of decomposition of BOD (d ), k, = rate of settling of BOD (d ), k. = reaera- tion rate (d"), and S, = sediment oxygen demand (mg/L/d). As indicated in Fig. P7.29, Eq. (P7.29) produces an oxygen "sag" that reaches a critical minimum level o, some travel time / below the point discharge. This point is called "critical" because it represents the location where biota that depend on oxygen (like fish) would be the most stressed. Determine the critical travel time and concentration, given the following values: 0, = 10 mg/L ka=0.1 d"' k = 0.6 d" k, = 0.05 d- L. = 50 mg/L S, = 1 mg/L/d