MATLAB assignment

You wish to design a plug-flow reactor for the production of the desirable product D according to the first-order reaction

A -> D with rate r_D = k_DC_A

There is also an undesirable side-reaction producing a waste product U,

A -> U with rate r_U = k_UC_A / (1+150C_A)

Where all concentrations are in mol/L, k_D = 20 s^-1 and k_U = 2 mol L^-1 s^-1

You have a pump that can deliver pure A at a fixed flow rate of 15 L s^-1 (which is 0.1 mol s^-1). The cost of A is $5 per mol-A. The undesirable product U must be separated from the product stream and disposed of at a total cost of $10 per mol-U. The resulting product, which is a mixture of A and D, has a value of $35 per mol-D provided that it meets a minimum purity of 95% (molar basis).

The reactor has operating cost of $(100+1600V) per hour, where V is the volume of the reactor (in L).

Solve the system and present the results. Determine the optimal reactor volume (L) and expected annual profit.