You are a Sales Manager with many responsibilities, and there are several sensitive market issue going on. You decided to go on vacation for 3 weeks.

Both A & D

Trusting the team and at the same  have a control over all situations is a good strategy that may ease pressure over the work.  This will boost morale of the staff also and make the team capable of handling emergency circumstances.

If I have good relations with Marketing Manager then I will definitely appoint him as Deputy during my vacations. 

 I wanna just to highlight that none of you thought about the Marketing Manager !!?? 

May be this confirms somewhat the gap between the Sales and the Marketing ??

  I will leave everything as is and manage my sales team remotely  and leave my mobile switched on all the time

My answer is First option  "A" and Second option is "D"

A & D only in case he or she couldn't make a decision.

YES ,  A. Appoint one of My  employees as a deputy with limited authorities and manage my sales team remotely  and leave my mobile/email /tab (whatever available) switched on all the time.

my answer is D...

 Sales Manager's activities and responsibilities are full time.  You can't afford to have gap or interval in these. Normally good Mangers keep training some of the bright person under them for some of their responsibilities. The wise advice is that he should go on leave assigning his responsibilities to one of his team members who is under training with full authority under his watch.  For crucial decisions he should consult him over phone but take his decision with full authority. It is even essential that when he is on leave he should give rest to his mind and body without much disturbance.

Choice B is more relevant to this situation.

I would go for option A, C & D