*Please do the PART B

Penicillin is being removed from water by solvent extraction using MTBE. The unit is a 10-stage countercurrent tower. Water phase with Penicillin W = 100 kg water/hr With 5 kg Penicillin/hr Extract Penicillin-rich MTBE 1 5 6 7 Recycled Solvent F = 13 kg MTBE/hr with 0.006 kg penicillin/kg MTBE 8 9 10 Raffinate Penicillin-lean water Solvent Pure MTBE S = 10 kg/hr As the first approximation with assume the equilibrium relationship at each stage to be: Y = 9 X (1) Where Y; = kg of penicillin in the MTBE phase per kg MTBE Xi = kg of penicillin in the water phase per kg water a) The solution to this problem is a set of 10 simultaneous equations. Derive these equations from material balances around each stage and the equilibrium relationship. Present these equations using compact notation. Solve the above set of equations to find the concentration in both the aqueous and organic phases leaving each stage of the system (Xi and Yi). Create a plot. b) If the linear equilibrium relationship is replaced by the expression Y; =9 + 20 X?, the solution becomes a set of simultaneous nonlinear equations. Derive the set of equations and solve numerically (Matlab's fsolve will work). Also plot the results