Chapter 16, Problem 9P

In problem 16.8, only one reactor is used. If two reactors are used in series, the governing equation for the system changes. Find the conversions for both reactors ( $x_{A2}\text{ and }{x}_{A2}$) such that the total cost of the system is minimized.

$\begin{array}{l}\text{Cost}=\\ C\left[{\left(\frac{x_{A1}}{x_{A2}{\left(1-x_{A1}\right)}^2}\right)}^{0.6}+{\left(\frac{1-\left(\frac{x_{A1}}{x_{A2}}\right)}{{\left(1-x_{A2}\right)}^2}\right)}^{0.6}+5{\left(\frac{1}{x_{A2}}\right)}^{0.6}\right]\end{array}$