[30 pt] In the dilute countercurrent extraction process depicted below, a stream containing a weight fraction yin of a chemical enters from the left at a mass flow rate of F1. Simultaneously, a solvent carrying a weight fraction xin of the same chemical enters from the right at a flow rate of F2. At each stage, an equilibrium is assumed such that K=xi/yi, where K is called a distribution coefficient. This can be solved for xi and substituted into a material balance for stage i to yield: yi1(1+F1F2K)yi+(F1F2K)yi+1=0 If F1=400kg/h,yin=0.06,F2=500kg/h,xin=0, and K=1.6, determine the values of yout and xout if a three-stage extractor is used. (Hint: develop the equations and solve them). Note that the equation above may need to be modified to account for the inflow weight fractions when applied to the first and last stages. Solve the matrix problem by hand (Use the algorithm that you think is suitable) and show the process