The board of directors of XYZ Inc. approves a $$50$ million expenditure for the company to sponsor a PBS program on "Earth: The Next Century." A is the show's producer; he is also married to B$,$ the CEO of XYZ$.$ Identify the strongest theory for a shareholder of XYZ to challenge the expenditure.

the directors violated a duty of loyalty because A and B are married, raising into question the fairness of the expenditure

the directors violated a duty of care, because spending $$50$ million to sponsor a show unrelated to the business of XYZ is grossly negligent

the directors acted in violation of their duty of obedience, since XY$\text{'}$s articles and bylaws did not authorize support of non$-$profit organizations

the $$50$ million expenditure constituted corporate waste, because the directors made no attempt to identify the show's value to the business of XYZ