Cost vs COP

Our cost savings analysis is indicating a different operating configuration than our best COP. Which is more important in this case? Should we go with the best cost savings and then just report the COP and Ts diagram for this case?

This is a really important question, and frankly it's quite critical to addressing the main deliverable in the task letter. Hopefully others will look at this as well.

The bottom line is to find the cheapest solution for the client; as with many engineering problems (and most situations) in real life, the almighty dollar drives everything. The client doesn't really care about the thermodynamic efficiency of the cycle, they just care about bottom line cost. So your optimal cycle and final recommendation will hinge on minimizing cost, not on maximizing COP.