Why any heuristic which is an optimal solution to a relaxed problem is admissible and consistent?

Because heuristic does not necessarily need to provide the best optimal solution. If the solution is 'good enough' to handle the current situation without causing any fatal damages, a heuristic is considered as successful
And on top of that, the stake in a relaxed problem usually not high, so handling it more than a heuristic could be considered a waste..

Hamlet's fourth soliloquy is probably his most famous one - "to be or not to be."it is rather different from his previous soliloquies because now he is contemplating something that didn't come up before - suicide. he is thinking whether it is worth it to fight to find his father's murderer when in the end all of them are going to die, so why not die sooner than later. he is contemplating if he should go on fighting or just kill himself and end it all, which is why this soliloquy in particular is rather depressing, hesitant, and gives a deeper insight into hamlet's madness.

The correct answer is connotation.