The design equation for this system is

for

. The solution obtained by using

*Mathematica*'s built-in function

Solve is

. Here

and

are the concentration of reactant

entering the first reactor and exiting the last reactor in

,

is the rate constant in

,

is the volume of each reactor in

,

is the volumetric flow rate in

, and

stands for the number of reactors. The cost for each reactor is

in dollars, and by combining the above two equations, the cost for

reactors is

. This function is minimized with respect to

and the results are shown for

and user-selected values of the outlet concentration of

,

, the rate constant

, and the flow rate

.