Chapter 16, Problem 8P

A compound A will be converted into B in a stirred tank reactor. The product Band unreacted A are purified in as eparation unit. Unreacted A is recycled to the reactor. A process engineer has found that the initial cost of the system is a function of the conversion $x_A$. Find the conversion that will result in the lowest cost system. C is a proportionality constant.

$\text{Cost}=C\left[{\left(\frac{1}{{\left(1-x_A\right)}^2}\right)}^{0.6}+5{\left(\frac{1}{x_A}\right)}^{0.6}\right]$