(a) Define the terms P and NP. Explain how the generation and verifications of solutions of an NP problem involve both P and NP. Construct and explain an example showing these characteristics. (7 marks) (b) Explain why a numerical optimisation needs constraints for solutions. Explain the effect changing the constraints will have on a numerical optimisation algorithm for finding an optimum. (6 marks) (c) You are running a Numerical Optimisation but each iteration is taking far too long to compute. After checking both the simulation and the optimisation algorithm you realise both are implemented correctly. Explain what the cause of the long time per iteration is, then determine a solution. Detail the effects your solution will have on the optimisation