Final answer:
In case of a corporate board deadlock, courts are likely to appoint an arbitrator or, as a last resort, order an involuntary dissolution of the company. Appointing a new director or holding directors in contempt is not within the typical range of court interventions. The resolution would depend on state laws and the corporation's governing documents.
Step-by-step explanation:
Resolving a Corporate Board Deadlock
When a corporate board like that of Ajax Co. has a deadlock, courts have several options to consider. They generally will not appoint a seventh director, as this could interfere with the company's governance and it is not within the typical power of courts to micromanage corporate decisions. Likewise, courts are reluctant to order directors to make an agreement or hold them in contempt for failing to do so, as it encroaches on the board's authority to manage the corporation. The most likely options are to appoint an arbitrator to help reach a decision, or in extreme cases where the deadlock is intractable and harming the company, the court may order an involuntary dissolution of the company.
However, before jumping to dissolution, courts often encourage parties to come to an agreement through facilitative measures like mediation or arbitration. This helps maintain the corporate structure and respect the directors' roles while still resolving the deadlock. Ultimately, each option depends on the specific laws of the state where Ajax Co. is incorporated and the content of the corporation's bylaws or other governing documents.