how to do this optimisation

[trish]

hello..i want to do optimisation of a heat pump...how to go about..i know engineering equation solver...what and how many equations in this?..plz help me formulate the equations...

 

i have attached the question below...

 

what assumptions do i need to make....

[Mr Skeptic]

You need to formulate the equation of the cost of the system. Then you can find the minimum by using derivatives. The derivative will be zero at every minimum or maximum, so if there is more than one place it is zero you need to check to make sure it is indeed the best minimum.

 

As for the equation, we're only supposed to provide some hints. Show your work first, and then we can help you from there. If you don't know where to start, you have to make sure that you have enough surface area for your heat exchangers, and consider there are also costs associated with the various temperatures, as they affect the performance of your heat pump. Since you won't know the optimal configuration, you want some of these to be in the equation as variables.