No replies to this topic

[Haematoma]

I could use so help for this particular problem. I have no idea where to begin. My original thought was to vary the input parameters until my profit converges to a solution, but that isn't working for me. Any thoughts or suggestion for finding a viable solution are welcome:

 

Here is the problem:

 

In making smooth chocolate as opposed to hard candy, you want to generate soft sugar( also known as invert sugar) from sucrose (which is a hard sugar that crystallizes by treating with an enzyme invertase.

 

rate = d[P]/dt = v = v_m = k₂[E]

where k₂ =(10¹⁵ min^-1)*exp( (-10⁴ K) / T)

 

The enzme decactivtes with time, especially at high temperature:

 

d[E]/dt = -k_d[E]

where k_d = (10₄₀ min^-1)*exp(-(3*10⁴ K)/T)

 

At what temperature, for how long, and how much starting enzyme should you employ to carry out the enzymatic conversation to minimize "profit" in a batch reactor, subject to the quality control constraint that residual sucrose content of 10% or higher in the final product is unacceptable? Assume the product is worth twice as much as the starting sucrose, and enzyme costs 100x more than sucrose?

 

Problem solution strategy is greatly appreciated.