A manager who says "I'll pay for it, but I want it as soon as possible" is considered to be:

E. would be the correct answer.

There will be additional cost premium for the urgent, I want it now at what ever cost.

A. Authoritarian can be too dominant and not as cost effective as they want their own way at what ever cost, so leading to almost correct, but NO, not my selection.

B. The manager is definitely risk accepting, as prepared to pay more, and the risk in finding a quick solution, it may not be the right quality, or supplier lack financial stability to offer warranty and long term continuing service.

C:Risk aversion is the reluctance of a person to accept a bargain with an uncertain payoff rather than another bargain with a more certain, but possibly lower, expected payoff.  There will be no bargain offering for an urgent solution. Therefore option C is incorrect. 

D. can never be right, as in business there is always solutions, only need to brainstorm and test all avenues.

D. in need of a solution  ^^^^^^^^^^^^^^^

D. In need of a solution. The manager wants to get his work done as soon as possible

D: In need of solution. At least not Authoritarian because in that case the person directs only.                                   

Correct answer is -   D. in need of a solution 

My answer is B) risk accepting 

is considered to be No : B.

B. risk accepting

B. risk accepting

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in my opinion  (D. in need of a solution ) is the answer.